>Is there a risk of bringing a smartphone with no past context on it (e.g. a previously-unused refurb or new phone)?

If you're willing to have two smartphones, or to backup and wipe your smartphone when you travel (don't forget the sim), then I guess not that much. I definitely couldn't be bothered though, hence the cheapie phone. Your mileage may vary if you're going for a 3 months sojourn I guess, I usually do 2-3 day trips.

However, back on the sliding scale of paranoia, the main risk of bringing your phone with you if you want next level protection from the US is that if they ever take your phone and remove it from your field if view, you might want to bin it. The US has proven very adept at modifying circuitry of devices to monitor them[1]. A cheap feature phone can be binned without thought.

[1] https://arstechnica.com/tech-policy/2014/05/photos-of-an-nsa...

factory reset will do the job even for forensic tools- the border-class forensic tools- cellebrite, magnet forensics aquire, oxygen, etc are all accessing above the flash translation layer. So deleted is deleted, in that case, on a phone. And chip off is Mossad level expertise, due to chip size/complexity, wear-leveling and said flash translation.