technically, yes. if you generated your key / created a new account on one of these websites, then yes, your private key is stored in your web browser cache. hopefully nothing malicious is reading that cache, but there is always a chance for that to happen. one nostr client has cross site scripting attacks back in november or december. it's absolutely possible.

i'd recommend taking your key and using one of the extensions that i recommended. then clearing your browser cache to get your key out of your cache.