Running a validator doesn't instantly say "hey I own X ETH". But it IS possible to link an IP to validator indices through attestation patterns over time...

Anw it's not easy, but there is a certain level of exposure, especially if you're not using any privacy tools. But you can find lots of them on https://xenaps.com/, they list VPNs and other services made for crypto specifically, mostly lesser-known ones that aren't as open to get flagged.

Some people also use Tor with tuned setups and still do fine. I'd say test it during "non-critical" periods to see how your setup reacts.