You can play game backups, use unofficial HDDs at bigger sizes, send over new games with FTP, use third party and DIY controllers like GuliKit's offerings or a Flatbox leverless arcade controller. You can play a modded version of Rock Band 3 with all the songs from all the games, using a Wii Guitar Hero controller with a Pi Pico-based adapter in place of the Wiimote. Any game you installed from disc for faster load times becomes playable without the disc in automatically once you get Aurora running (this is pretty cool, on some other modded consoles like PS4 you'd have to reinstall the games another way).

As far as homebrew in the sense of people making their own games and applications, I don't know that there's much going on. Maybe you can find a controller tester app. Sadly the 360 scene has a lot of proprietary stuff going on, and uses some official dev SDKs, IIRC. Where 3DS and Switch modders have everything on GitHub and freely licensed, 360 has a lot of binary-only releases on random forums and such. It would probably be a major effort to change this and involve rewriting stuff people already know and love.

I did the the RGH 3 mod to half a dozen or so 360s a few years back for myself and friends. If you just wanna play games with modern comforts, things are in a pretty good state. We don't need to worry about the original disc drives, HDDs, or controllers wearing out and making the console useless, we can replace or avoid them all. The wireless card is also easily replaceable, a friend of mine had one that seemed non-functional after he spilled some Mtn Dew all over his 360 back in the day. Everything else seemed good after a clean but I just got him a new wireless card off eBay and swapped that out.

If anyone wants to get into this and doesn't already have a 360, the S models are easiest to mod and most reliable (no RRoD). Some are Trinity and some are Corona motherboards inside, but both are hackable. Corona may need a post-fix adapter, but they're cheap and easy to install. Just avoid the E series.

For modding tutorials, MrMario2011 on YT is great.

There is also a software-only exploit that's a bit worse but more accessible. It came out after I already did all my modding, so I haven't got experience with it.