Name one and describe the process. So far everything I have tried takes hours and often loses a bunch of settings that need to be restored manually. It requires significant amounts of work. Also it seems most tools need a rooted phone
A minor inconvenience given the legal risks. If you don't want to deal with that just get yourself cheap used gear dedicated to travel purposes.
I have used the built in backup to Google and noticed that restore takes many hours and a lot of apps lost data and settings. It took considerable effort to get back to normal. Definitely too much work to spend on my first day of vacation.
A burner phone may work but then you don't have access to all your data.
If you install TWRP recovery (root is only required for the installation, not the maintenance), you can do a full-phone backup.
There are plenty of backup tools available on the internet, this isn't really a problem with Android. Personally that's what I do each time I travel abroad. Both because I might loose my phone/laptop and because on can never be sure what software/content is legal(or not) in this or that country.
Some people got jailed abroad for content/software that would be deemed legal in my home country, on their computer.