yes, it currently should auto detect a browser extension and show like that

Keychat Browser has implemented NIP-07.
https://github.com/nostr-protocol/nips/blob/master/07.md
For example, when you use a Nostr web client such as Jumble in the Keychat browser and choose **Extension Login**, your Keychat IDs will pop up, allowing you to select which one to use to log in to Jumble.
yes, it currently should auto detect a browser extension and show like that

I understand your point, but I’m not sure at which stage the problem occurs.