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.
have played for an hour, works good was greeted with a screen to select between rwo graphics presets for the deck.
ich habe völlig umsonst einen halben Roman geschrieben?!