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.
On the other hand:
Most Frontends are not super interactive google tables like applications and never will be and frameworks won't magically make your code maintainable or enable you to work with 50 other guys on that page that interacts with a simple CRUD-API, yet people choose a complex framework meant for huge projects and pile even more dependencies on to of it for that kind of stuff. it's like using a fleet of 18 wheel trucks for grocery shopping, when a basket and a bicycle are really all you'll need for that.
i'd guess most websites would be fine and feel "modern" with html, css and a small library for ajax stuff, because doing that by hand is repetetive and error prone.
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.