https://www.consilium.europa.eu/en/infographics/schengen-bor... says "ETIAS and the entry/exit system do not apply to nationals of Andorra, Monaco and San Marino and holders of a passport issued by the Vatican City State or the Holy See". Those are all microstates entirely surrounded by other countries that are part of the Schengen area.
Ok, so, The Great Race 2023 a sporting program where competitors try to get into as many of these non-schengen countries in Europe without requiring ETIAS to do so.
Can one balloon across a country without requiring a passport?
I guess a diplomatic passport would make you immune from requiring ETIAS. Those can more or less be bought from some countries (e.g. from the USA. Heavily sponsor a president’s election and before you know it you’re ambassador in some European country)
Alternatively, apply for asylum in one of the countries and start traveling to other EU countries (that’s not allowed, but not because it requires ETIAS, I think)
Also, parachuting in is relatively easy, but how do you get out?
You are reading it backwards. Citizens of those countries don't need this waiver to travel into Schengen countries. The other 59 countries who can currently travel visa-free will need the waiver.
I guess aside from those, countries in Europe that are probably not requiring ETIAS, Great Britain of course, Bosnia, Croatia, Macedonia - the countries that once comprised Macedonia. So I guess if you can get to those countries without passing through EU you're ok? Just a guess though.