In online communities such as the StackExchange network, many people use images of their favorite movie or comic characters as profile images/avatars.
In the US, this is apparently legal due to the "fair use policy" (cf. Is it legal to use movie frames or actor images as online avatars?). However, "fair use" is a US concept for which (to the best of my knowledge) nothing similar exists in the European Union.
I remember researching this particular question with respect to the legal situation in Austria, and came to the conclusion that the right of Privatkopie ("private copy") does not apply, since making the copy available publicly is explicitly forbidden (§ 42 Abs. 5 UrhG).
This, however, was many years ago, and, in the meantime, a lot of EU legislation on copyright has been passed, which might override national legislation. Hence my question:
In the EU, is it (currently, 2021) legal to use a copyrighted image as a "profile image" (i.e., a low-resolution image shown next to your user name for illustration purposes) in online communities without permission from the copyright holder?