It varies from country to country. Mostly there are spot checks.

But May 2022 is an eternity away. Nobody knows what rules will be in place by then.

Use reopen.europa.eu as a starting point for information on COVID-related travel rules.

What applies now will be of no use for then. For better advice also quote nationality and the countries where you stay/have been and want to visit-rules differ per case.

4 month will pass quickly and I am just trying to get a pulse on current conditions. We traveled to Peru in May and that was tricky it’s hard to grasp what traveling by train from country to country will look like. All reply’s and suggestions are greatly appreciated. 

My wife and I traveled in Europe in October-December. We had no problems with the certificate of two vaccinations. However, it was a time before the omocron and new restrictions.

Our experience has nothing to do with you in the next six months. Follow the situation, you have to decide for yourself what to do.