Hello everyone so after this long, I managed to find a solid but unsettling solution.
In fact, it is a big software issue making me even wonder if it was set on purpose just to prevent the phone from heating. The game driver that came with android 10 ruined its gaming performance, and setting it to "focus on perfomance" will not make your fps any better. I just hope they won't apply it to non-gaming apps too in future updates, otherwise there will be no fix for gaming and the phone will perform very poorly.
So, my take on it was to install a VM (Virtual Machine) using VMOS Pro (no root needed). You might think this is not suitable for gaming as it will take more ressources than a real machine, but actually the hilarious thing is that the game is way more fluid on the VM.
Note that your in-game sensitivity might need to be changed, which is still confusing me.
Disabling HW overlays in the VM's developper settings might help too.
Thereby, I think that this is just a way to avoid using the game driver of the phone by running the game as a normal app inside VMOS Pro.
However, as you can tell, a VM will never perform as well as a real machine. But in fact, I ran Geekbench 5 on both the VM and the real one and the scores are not that far (1300 against 1500).
Imagine running the game without having to run a VM, it will be flawless, how unfortunate.
Special thanks to VMOS.
I hope it worked for you.