OK, I ran mongod and from the error output it appeared that the culprit was /tmp/mongodb-27017.sock from the following error:

{"t":{"$date":"2025-02-03T23:13:06.391+00:00"},"s":"E",  "c":"NETWORK",  "id":23024,   "ctx":"initandlisten","msg":"Failed to unlink socket file","attr":{"path":"/tmp/mongodb-27017.sock","error":"Permission denied"}}

So I removed the socket file, uninstalled and reinstalled mongodb, and now mongosh connects as expected.