Assuming it is the right temp for rain there should be a rainforest and quite a big one.
This also assumes there is enough water but not so much its just an ocean.
Something similar creates real rainforests on earth, See a Hadley cells
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/vXTic.png)
Rising air is where most rain comes from. As warm air moves along the ground it picks up moisture. As that warm moist air rises the potential to hold water drops because the air cools and its pressure drops as it rises. So moisture in the air condenses out as the rising air becomes supersaturated as saturation potential drops. Its basically a ring shaped Hadley cell. this should be the place were the most rain falls.
Cloud cover will be an issue, since these clouds will shield the ground below it, the warmest point on the planet should be constantly moving, meaning you may actually get something like weather with clear days and storms near the calculated point.
The other consideration is erosion, the erosional forces in the area will be huge, unless the planet has active tectonics or its not perfectly locked this area should erode until it is uniformly flat. So there actually may be a shallow sea, so more like a mangrove forest, but only if the planet has been locked for a LONG time.
The only problem you will have is is there enough moisture left for rain in the first place since most of your moisture should freeze out on the cold side. But if you have enough water to get rain, this is where it should be falling.
It is worth noting a tidally locked planet still rotates so Coriolis effects still occur. It just rotates once per year so the effects are not very strong. This will help cause disruption to the air flow and means the rainforest will not be round but more football shaped.
Useful take on the problem. https://worldbuildingpasta.blogspot.com/2020/12/an-apple-pie-from-scratch-part-ivd.html
How circulation works on a tidally locked planet.
Ditto
https://www.pnas.org/doi/10.1073/pnas.2022705118