Code Health: follow ups from connection restarting

[zadjii-msft]

From #14060. See also https://github.com/microsoft/terminal/pull/14060#pullrequestreview-1165989506

The control shouldn't be responsible for restarting the connection itself. It should request a new one from the app.

• [ ] Move this code to the page, and bubble an event to request a new connection
• [ ] Revert this
• [ ] Investigate only clearing the buffer to scrollback, instead of inheritCursoring

[zadjii-msft]

I very much want to punt this to 1.18. There's a lot of stuff that I built for tear-out which will make this a lot easier to manage.

Now, we have to like, raise an event up to the Pane (who is hanging on to the Profile for this control), to ask the TerminalPage to build a new connection (because TPage alone knows how), then wire that back into the control

But tearout branches have more elaborate ConnectionInformation that we could just stash in the ControlCore and reuse immediately to build a new connection.

I wonder how painful that "backport" would be...

dev/migrie/b/cxn-restarting-attempt-1-backport has the start of this