Just being open source is not enough to solve this problem. You would need a record of your “home instance” stored somewhere that Lemmy would always have access to it. You can’t use browser storage or cookies, because that’s restricted in browsers on a per-domain basis. The browser extension has its own storage so it doesn’t have this restriction.

I can’t think of an architectural solution to this problem without a browser extension.

The closest alternative that could be upstreamed is what Mastodon does, which is prompt the user to enter their home instance every time they try to interact with something while not logged in. An upstream solution can never be fully automatic like a browser extension, but this may be “close enough.”