“Reasonably priced” is relative, of course. You can get a used Pixel 6 on eBay for $160 and put GrapheneOS (free) on it and it would probably serve you well (this is my current daily driver). There is some (rather esoteric, I’d think) risk to using a used phone even if you wipe it first, but I don’t think you’re likely in that territory.
It’s popular to use the term “burner” to describe a cleaned-out phone, but it isn’t necessary to actually burn the phone after you’ve used it for a trip (unlike the phone you use, say, to make ransom demands after developing your world-destroying superweapon). The Pixel 6 still has at least a little life left in it, so it wouldn’t be a consumable expense.
I suppose there’s some risk that just having GrapheneOS marks you as someone with Something to Hide™, but I’ve not had any problems with that. Unless someone actually hooks up a Greyshift or some such to your phone, they’re unlikely to even notice that it isn’t stock Android.