Of course you can! No problem. Trains run mostly as normal.

Only in the far south east of EUR, the Balkans (think of Serbije and surrounding countries) most INTernational trains are cancelled. THUS: there are/were in fact NO trains at all from GR to Hrvatska=Croatia. But that was already nearly so before the pandemic came. Use a general EUR-wide travelplanner for trains, like of bahn.de (this is german railways, it works for nearly all of EUR). The planner of EUrail is often incomplete and not regularly updated.

As for now, this week, in several countries there are also many cancellations due to high level of sick staff. But that usually means that on a certain line the trains now run every 30 in stead of 20 mins.

You do, if vaccinated+Booster, in general not have to make new tests all the time-only a very few countries still want that (f.e. ITaly). BUT you beter get a EUR QR code as the checks are more often for HTL or Restrt-as a tourist you cannot really avoid that. In SOME countries (DE,FR,IT) you also need to be able to show this on board trains-there are spot checks every now and then. But this all can change by the minute!

Most borders are open but with spot checks for the COVID requirements. Check reopen.europa.eu for each country's requirements. They change regularly with little notice so also check shortly before travelling. If you're only travelling in a few months’ time, then it's no use looking at the rules now because everything will probably have changed.