I am considering staying in Monaco, San Marino, or Vatican City before I can enter the Schengen area again.
According to this answer, it is valid to stay in these three micro-states in order to stop the Schengen clock.
However, also according to the answer:
Problems will arise when the visitor ultimately leaves the zone and must undergo a Schengen exit inspection. At this point the person may be asked to prove that they are not an overstayer and the border guard will be entitled to see hard evidence in the form of official documentation. There was a case where an individual attempted to show that his mobile phone registered to a tower outside of the zone and this failed obviously: radio waves have no respect for nation borders but also one could mail the SIM card to a friend in a far away land, put in a phone where it registers to the tower and then mail it back. Apparently hotel receipts can be too easily forged to be successful as evidence.
What the border guard will want to see is a passport stamp from the local constabulary. But the constabulary is under no obligation to issue one, so success is down to personal impact and articulation skills.
I'm not sure if I could get a stamp from the local constabulary. However, I always use AirBnB to stay, and the reservation email and the mobile app might be far more reliable than a random hotel reservation document.
So, does the AirBnB reservation email work as a proof of staying there? Or is there any better document as a proof of staying ("better", in terms of ensuring that I don't pay the overstaying penalty)?
I will likely leave the Schengen area ultimately from Frankfurt International Airport.