TBH, buying a cheap Chinese burner phone with no security relevant data on it just for traveling to the US, might be better security wise than buying an expensive Google Pixel Phone with GrapheneOS on it.
Especially now where Google, a US company and bound by its laws, that produces these devices, might (start) hand(ing) out backdoor keys to their hardware.
But with Graphene&Co you can make full backups, store them externally (e.g. selfhosted cloud) and then just apply before/after crossing borders as needed. Plus doing that makes a duress wipe way less painful if you ever need to. Tho, if you're somewhere where they're likely to just keep it instead of forcing an unlock or copying data, a cheap burner that doesn't hurt to loose is still the better idea...
That is a good option. I am actually quite careful about what I use my phone for. I still on occasion use Google maps, but i turn location history off and I always delete previous searches.
I am aware that this does not remove them from google's database, but it does make your movements not immediately obvious.
Also i would delete browser history and log out of all social media accounts (and disable remembering usernames/passwords) and even uninstall some apps in order to make who you interact eith less immediately obvious. Once you clear the border fully you can reinstall everything at your earliest convenience.
*Proton had a controversy involving the CEO claiming "Republicans are the party that 'fight for the little guy'" so... do your own research. But they are also the best when it comes to amount of servers, so its less likely to get blocked by websites.