Remember what site you actually ran a query on in history and allow re-running on that site

[TuggyNE]

Used to be, SEDE would always only link to the query for the site you actually last ran it on in history. That was often useful, but there was also a fair use case for just running it on the currently selected site, since usually that's what you'd end up doing anyway.

Recently, SEDE seems to have switched over to favor only the latter case. I'd like to go back to the earlier behavior, or, if possible, add an additional link (parenthesized or otherwise deemphasized?) with the original site. That way the primary and secondary use cases (current and past, respectively) would both be well supported.

Originally reported at Meta SE.