Animals and fungi consume other biomass instead of creating their own, so the basis for this goal will be plants.
Ocean has a few kg of biomass per m2, while forest orders of magnitude more, especially if you count the soil. Oceans are bad mostly because of how easy it is for animals to eat the algae on a massive scale, and how little algae could do to fight it. Herbivore activity in a forest is significantly harder. So there has to be as few oceans as possible and as much land as possible. Mountains have even less life than oceans, so they have to be minimized as well. Planet must be flat.
Large CO2 proportion promotes plant growth, so it has to be maximized. O2 promotes animals and fungi activity, so it has to be minimized. Currently plants need O2, but newly evolved plants can store it or hibernate over night. It also speeds up erosion, that frees nutrients from rocks faster. N2 is somewhat beneficial, but no need for such a large proportion. Larger pressure is preferred for more rain but detrimental to the atmosphere transparency, at 3 atm transparency will drop below 50%. Optimal atmosphere as I see is 50% CO2, 50% nitrogen, 0% O2, 3 atm.
Optimal star would provide most visible light for plants, UV for restricting fingi and animals activity, least IR to avoid overheating. It has to be a big star. But bigger stars run out faster. Just 1-2 solar masses is the high limit, to have a lifetime over a billion years for evolution.
Big rocky planet provides more surface gravity. This is beneficial to remove mountains and deep oceans. This is also beneficial for thinner atmosphere for ease of cooling. And beneficial for having more land area. And planet interior cools less, allowing more time for tectonic activity. And more volcanoes allow to emit more CO2, provide local patch of new nutrients, destroy old habitat locally, allowing to keep biodiversity and allow for evolution to happen, make volcanoes more local and less global event. I dont see a limit to this property, other than having too big of a planet might be unlikely. For 1000 earth mass and similar density, surface gravity will be 10 times larger. This also helps making locomotion less beneficial in general, more costly, prohibiting most animal activity. This hurts plants as well, requiring them to be stronger, but since question was 'per planet' rather than 'per area', I will keep it. Such a planet would have 100 times more area.
Any way to increase nutrient flow is beneficial. Meteorite shower is one way, but in most cases it is very time dependant, and is either too active or too passive. Having another planet nearby, close enough to provide tidal heating, that would increase volcanism, has no such problem. For it this second planet must be at least as massive. So a double world or a gas giant, both will do. It must be not a star, otherwise cooling wont be possible. And it must be as close as possible, to provide most tidal heating. Water tide also helps evolution.
Surface temperature optimally be about 50 C. So that water is not boiling, but not freezin either. This also helps to provide the most water vapor possible, most rain. Some animals have temperature close to that, so in terms of biology it seems ok. More temperature allows for faster life. It means decaying matter will be destroyed faster by fungi, but it means faster evolution, and that is likely more beneficial - more evolved ecosystems are heavier per area. Probably colder planet could have more biomass if its massive soil would consist of centuries worth of dead plants, that all can be considered biomass. But risk of glaciars seems more significant judging by our planet, so I will go with a safe route, warm planet.
So, here we have it. A swamp planet. Hostile to most life as we know it, incluidng humans, but containing the most biomass.
