When I travel presumably I'd want to have a smart phone to take pictures, check internet (maps, recommendations, itineraries, etc) and to make communication with people back home or people I'm visiting.

What would be the best way to protect myself with a phone while still being able to do all of this? Having a burner smart phone with an ESIM so I keep my number (for communication), itineraries saved to device, and no account logins or apps?

You don't need a dumb phone, the only important thing regarldess if it is a dumb or smartphone is it has to have been reset, without any google/apple/social account. You may just put the number of your parents and significant other if you are fairly sure they are not partaking in any activity (even associative) related to human rights, journalism, environmentalism, science, aren't working for a company that is currently in trial or whose headquarters are in a country with sanctions or tariffs and/or aren't public persons. But you should really know the number of your close relatives from memory anyway, it isn't that hard.

You can access some data remotely afterwards but I wouldn't restore it and make sure it doesn't stay cached on my devices. Better to connect to a remote desktop with credentials you know from memory. What you could do is find some recommendations for a good lawyer in the area you plan to go beforehands and have his number stored somewhere.