The best way to figure out what motivates your creature is to consider the constraints it lives under.
First, let's see if your creature can get the energy it needs. An average person consumes about 2000 calories per day (food calories, or 2000 kcal). That's equivalent to 2.3 kilowatt hours of power.
Energy in sunlight at the equator is about 2300 Watts per square meter. A human has about 1.7 square meters of surface area, but only half would be facing the sun at best. Let's say it's a big creature, and therefore has 1 square meter of surface area facing the light.
The most efficient plant at converting solar energy is sugarcane, and it converts 3.5% of light into energy. So the available energy to the organism will be 2300 Watts * 3.5%, or about 85 watts. So to get the amount of energy that a human consumes in a day would require your creature to absorb 27 hours of direct sunlight, assuming the sun was as bright as the Earth's at the equator.
But that's a very, very optimistic number. Every detail from there makes it worse. For example, maximum solar efficiency requires that the collector be tilted to the angle of the sun. Then there's cloud cover, and shade, and...
On Earth, a large tree on average collects maybe 200 calories of energy in a day. That gives you an idea of the real world efficiency of photosynthesis.
My understanding is that a tidally-locked planet close enough to a star would have any water evaporate from the day side and freeze out on the night side. If the planet is far enough away for liquid water to exist on the day side, it's not going to get nearly as much solar energy. On such planets, the only areas where a plant species might survive would be along the terminator, but the solar energy on the terminator would be much lower. Also, there would be a lot of clouds in that area.
On a cooler tidally locked planet you could have water on the 'day' side, but probably only if there was enough water for a global ocean, because the water on the 'day' side would be melted ponding on top of the ice. If there wasn't enough water to go around the globe, it would still all be transported to the 'dark' side where it would freeze out into a permanent ice cap. Perhaps on such a planet there would be a larger habitable zone along the region where ice turns to water. Again, you would expect lower solar energy there than at the hottest place on the planet.
There might be a way around this - we don't know much about such planets, and there are probably variations we haven't thought of. But it will take some work in planet design to come up with an eyeball planet that can host sentient plant-creatures.
But I think that's still do-able. Your people would have to be large, spread out, maybe with leafy sprouts all over to maximize surface area. They'd probably also be slow moving and slow thinking, as thinking takes lots of energy.
Consider creatures like a Tree Sloth. A Tree Sloth only uses about 110 calories per day. So a large, slow-moving creature with lots of surface area could possibly work.
What would motivate such a creature? Lots of things. For example, first contact with a faster thinking, faster moving species like us. Or a natural disaster, such a plague of mites or bugs that starts eating them, requiring them to up their game. Or another natural problem such as drought or CO2 depletion.
If you are asking what motivates them as a species absent any external shocks, that's a bit tougher. Why would such a species evolve intelligence in the first place? What problem does that solve?
Perhaps they have a symbiotic relationship with another species that can tolerate heat better. Maybe there's a type of vine that grows underground for long distances, then sprouts where it's hot and very bright. The symbiosis is that the sentient species provides water to the vines, and the vines return nutrients for the people or something.
Here's a potential idea: They are networked. Rather than move around and consume energy, they are motivated to connect to each other either through roots or temporary physical contact. Because if they can share their chemical resources and concentrate them , they can advance and prosper.
Perhaps they all started out equal and non-sentient, but once they started connecting together some evolved the ability to extract extra nutrients from the network, and they became smarter and faster thinking. Eventually they all became sentient, but the creatures in the 'super clusters' in the network get more than their share of energy and therefore evolved more intelligence to manage and improve the network.
That creates a society where the powerless have more than their share of energy extracted for use by the 'advanced' ones. So you have armies of plant people who move slowly and without much thought, providing their photosynthetic energy to the 'haves' who need it to think at higher levels. This creates a stratified society where only a few plant-people can really think and work at a high level, but only because the majority have to do with less than they would on their own. But it's stable because the powerful ones do more good for the society through invention or organization that the individuals could do on their own. An analogy would be an anthill with lots of workers, except the 'work' involves optimally spreading out to collect as much light as possible. This feeds energy back to the 'hive', or cluster of higher-level members of society (although in an anthill that's not true - queen ants aren't any smarter than any other ants - they just use the excess energy to breed more). Still, the same idea - masses of creatures that aren't motivated to do much more than find good places to spread out and relax, and their thinking is constrained by lack of energy. In the meantime, creatures in the 'hubs' have plenty of nutrients, so over time they became smarter, faster, etc.
Then one of the smart ones invents a new energy source the masses can use to bring themselves up to the same level. As this tech spreads and members of society can supplant their own photosynthesis with extra energy, they start to think better and faster, and decide they no longer need the 'smart' ones. And the 'smart' ones are going to do everything they can to hold on to their power over their society. Wars break out, etc.