The Lexicon description of the links property of sh.tangled.actor.profile says:
Any URI, intended for social profiles or websites, can be used to link DIDs/AT-URIs too.
But when you try to set an AT URI like at://did:plc:xhvreb3sb62k5u73jkjt64jr, the tangled.org web client displays an error like so:
Invalid URL 'at://did:plc:xhvreb3sb62k5u73jkjt64jr': parse "at://did:plc:xhvreb3sb62k5u73jkjt64jr": invalid port ":xhvreb3sb62k5u73jkjt64jr" after host
And when you try to set a DID like did:plc:xhvreb3sb62k5u73jkjt64jr, it gives an error as well:
Warning: URL 'did:plc:xhvreb3sb62k5u73jkjt64jr' has unusual scheme: did
If you directly update the profile record, the profile doesn't seem to get updated on the AppView's side.