Record credential picks for this chat

Keep the account the user chose on a connect card for the rest of the chat.

The card shows one account and the tools used to re-match on their own, so with two accounts for a provider a run could land on the other one. The tools now use exactly what is recorded here, and ask when several credentials qualify and nothing was picked.

Every id is checked against the caller's own credentials and the provider it is filed under; one bad entry rejects the request and records nothing.