add it to steam as a non-steam game , if you use that for other games, and try to create a mapping with Steaminput. I have not done that for fallout, but that offers so many options that i am certain you’ll be able to map everything to your controller you need.

If steam is not an option xpadder or joy2key might work for you, but i have not used them for ages.

into the breach is fine on mobile. there are also some games that would be good on the tv with a controller like dead cells, but atleast they dont offer games via the fire tv stick app, dont know if i could download them on something with android proper.