Refactor how connection restarting is handled

[zadjii-msft]

Admittedly, this is a lot of annoying plumbing.

We didn't love that a connection could transition back in the state diagram, from Closed -> Start. That felt wrong. To remedy this, we're going to allow the ControlCore to re-create connections, all on its own. This builds on a lot of work that was originally done for Process Model v2 (#5000), and was originally slated to be merged in #12938.

Basically, all the properties for a Connection are stashed already in a ConnectionState object. We're gonna take that, and stash the info in the ControlCore. When the control wants to restart the connection, it just uses that to rebuild a new one.

Cleanup from #14060

Closes #14327

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[zadjii-msft]

Closed in favor of #15240