Burner phones aren't safe. Security through obscurity worked with the 1990s cell network but not with today's vast logging/geolocation tagging.
This is all well documented
https://www.offgridweb.com/preparation/burner-phone-basics-h...
In Estonia, you could buy a prepaid SIM card in a convenience shop a few years ago, without any sort of ID verification. Not sure if that’s still an option but I think it’s not a priority there. You can then use it all over the EU.
And of course, buying a phone without a contract doesn’t require ID either.