Great, the addition of the secret will be a big improvement.

I tried connecting with multiple relay implementations (nos.lol which is strfry, bucket.coracle.social which is coracle/bucket, relay.nostr.band, relay.noswhere.com, and relay.stoner.com which is nostr-rs-relay), but none of them gave me any responses. Anyway, the same flow works fine with nsec.app.

Are you testing this on coracle? If so, make sure you're on dev.coracle.social, which has a whole bunch of bugfixes.