Nice, you know your shortcomings, nice definition of what passes and what's not.
While it probably possible to imagine a creature which can do as you want - hop from a gravity well to space periodically, doubt it can do it frequently however, as even few times is somewhat an achievement.
We may probably imagine them being able to produce carbon nanotubes natively, as part of their tissue, 100GPa tensile strength and thus being able to accumulate required energy over time and then use atmosphere gas and (or) water to propel themselfs like a typical rocket. Or even rocketfuel, without cryo to it, and be in essence a rocket.
However it probably just a good(or not, taste preferences) handwavium
More realistically, on the border of handwavium it can be a part of some maturity metamorphosis, when a bigger body shoots out its part(s) in to the space. There are real proposals of gun like solutions which should be capable to shoot a ton or so in to space, and it looks viable. But sure mass of the gun and mass of a projectile - one is much bigger than another, but there is a certain simplicity to installation, it just long, km's long.
- km size organisms are not common, but some forests are one tree actually(or something close to that), so not impossible. So some photosyntetic organism, without necessity to move that much, maybe, but not only.
And those guys, which are shot to orbit, they do not travel that much of the orbit of the planet, they hunt for those spores to grow, and that this bigger ground body lives by itself long enough to shoot many of those projectiles, with nanotubes and such it may endure more than one shot, plus healing, and other ways, etc. Projectiles, those shoots, are some sort of spore witn a shell, so as it is food for those in orbit, so as it can become some sort of parasite, which sticks to already grown thing in an attempt to consume it, and some times it just kills kessler syndrome like or just by a collision.
So when they grow enough, those who survived it all and were in luck they may choose to get to higher orbits, to avoid being shot by a parasite thing or collide with others, and maybe later they evolve in something which travels a little bit more.
Ecosystem of those wont't be so chil, as you seems anticipate, it will be harsh bloody massacre in slowmo over 1000's of years, a blood bath from which rare surviviors will emerge and wander off. The thing will evolve sloow, but it can be engineered.
So situtation can be quite complex. So easier it is to handwave the first option.
So while it is not impossible to imagine such thing, hard to anticipate it to evolve, but who knows who knows, and I guess there is a chance to make such thing to be.
- "can be a part of some maturity metamorphosis" whichever way you do it (gun or rocket) it necessarily loses a large portion of its mass with every ascent into orbit and beyond .. so one way or another whatever method is chosen it can probably be viewed as this to some degree, it's going to require a long growth period to replace the parts used for each launch whichever way you go .. if the OP was using a smaller gravity well things could be different. – @Pelinore
About how long it takes to recharge. Due the size, photosyntesis is the most likely as an option, not necessarly the only one, especially if we talk about artificial creature, but for evolved one it is a most likely option.
In earth conditions, 100x100m plot of land can bring about 2 tonnes of fuel, in form of grass itself, so if we wanna some juice from them it will be less. So, the thing grows some sort of "limbs" getting 2t of fuel per season is optimistic scenario. And so for "just" 2000t (Falcon level, not exact number, with just 5-10t payload to obit) it will take 1000 years of milking that 1ha plot of land. Sure it takes less time to grow bigger, and 1x1km may spedup things to a decade or few(there is time required to collect energy to grow those limbs over that bigger area)
All in all it decades between recharges, not a thing to do at wimp, unless it is some from of gray goo and it more tuned to this kinds of things, which can be if it designed.
PPPS speeds and feeds of patch/"limbs"/energy collector growing
- "100x100m plot of land can bring about 2 tonnes of fuel" Hmm 🤔 perhaps we might consider a fungus, or something that shares some of its characteristics, this one covers 5.5 km subsurface with its Mycelium –
Growing a patch takes some time. If we take grass as our example, then it grows about 1g of dry material per meter per day, there is root system as well which also should be grown, let's say it almost the same size/mass as what is on the top. And full grown system is about 400g per m2
- grass is used in the answer, and elswehere in the post, only to estimate potencial of speed of growth or speed of producing useful chemicals("fuel"), just because I know some numbers about it, but by itself it not necessarly a best syste, however one of many possible solutions it may as well just look as an regular grass patch, but it does not mean it is your regular grass patch, or that it should look like one in other cases. But less stuff one has tk grow faster things go.
speeds and feeds
If we take our grass model as studu case then close to a best speeds case, speed of growth, how much it covers, doubles each year/season (not a strict calculation, but some approximation), then if it starts with 1m2 then it covers 1ha in 13-14 seasons, 1km2 - in 20 seasons, 100km2 - in 26 seasons. Exponencial growth rate, and artificial system can do that.
Real grass patch probably grows more linearly, like proportional to circumference/perimiter of the patch - so it more like linear speed 1m per season, and 1ha is then in 50 seasons, 1km2 in 500 seasons.
- real plants use seeds as well, to speedup, which are carried by wind or animals or..
So depends on strategy, and abilities of that organism its time to expand the means of collecting energy something in between those numbers.
And depending on how much fuel it needs and speed of growth it will have some typical size as optimim between the speed of expansion to collect more energy and energy flow due time of that expansion.
I mean that it all depends on events whjch have place in the system, for cases when we optimize it for time, there is an optimum between how much to invest in system which collects energy, and how much energy to extract after that. It typical EROEI, almost a definition of it, and specifics of what is actually optimal, is not an easy question, but at least it easy to say that be huge huge huge humongous big is not neccessarly a best strategy for all cases. But something up to around 1km2 may be a reasonable number.
types of plants moss, grass, bushes, trees
As for which plants to model after, all those 4 categories have their advantages and disadvantages in this situation, and it depends on climate and environment. Trees are good to extract stuf from depths, but they are expensive energy wise per square meters(poor EROEI). Moss is cheap energy wise to cover surface(good EROEI) but poor at extraction of water from depths so it grows in naturally moist environments. Grass and bushes are somewhat in between.
Each of those potencially can create root system, but some horizontal tree like structures look like an solution in this case which nature and skme designs could take, as it needs channels of considerable sizes to collect stuff in a central location. Maybe more like lianes, on the ground. Just interconnected regular root structure won't do the job as it has other goals. (Tree roots have the goal to gather stuff to a central location - so it a good model)
So as layout it may look like a mold from a top(or like a tree leaf), as strucutre elements it lianes(big diameter closer to collecting point, branching out like in a leaf), grass bushes as main energy collectin element. And its size pretty much unlimited, and only limited time how long it it sufficient for it to collect what it needs.
But it just one of the potencial options, there is some variety of what kind of shapes it can potencially take to solve energy collecting problem.
Parasitic properties to solve the problem, liane like, looks like a good strategy in the case, if there are forests to exploit, etc. That all is a deeper level of speculation.
Consider things only on energy level, to a certain point is a lesser speculation, or if we skip which specific shape a solution takes then it is close to be not a speculation, because we rely on conservating of energy law, physics and such things.
Specific solution it is a design work, and it can take multiple shapes, and is more subjective, to what people think is more viable or less viable.
All in all - all kinds of specific solutiins can be reasinably imagined in this case, and which one is better realy depends on an environment, to which we have no knowledge about.