The main issue is that they have the authority to deny entry and to detain you for basically any reason they can come up with, and it's been shown that they won't hesitate to do either or both.
So if you really must travel to the US, you need to comply. Your best bet is for your phone to look normal enough, and not have anything they wouldm't like on it.
If the games you're looking to play are competitive multiplayer games, those usually actively fight Linux users. Games like Valorant, Apex Legends, and Fortnite are all broken on Linux due to their invasive anti-cheat software. There are exceptions to this, of course. The devs of Marvel Rivals, for example, have said that they don't have a problem with players on Linux.
For.anything else, odds are it will work fine. You can always check protondb.com to see if, and how well, your games work under Linux.
I've been Linux-only for a few years now, and I haven't had issues playing anything yet, besides maybe some minor tweaks.
Mods can be more complicated, but I don't have much experience with that. I do believe Nexus Mods are working of a project to simplify game mods under Linux, so hopefully that works out well.