Testing: Pet persistence / notifications across sessions

Testing https://github.com/microsoft/vscode/issues/327558

I had similar feedback as Kyle:

> I would think of it as one persistent pet that stays with me (and could maybe even get my attention across sessions -- i.e. if a different session needs input, it can help point me to that)

I wonder if a user could configure if they'd like the same persistent pet vs unique ones tied to each session?

I also wonder if the pet could have a small text speech or thought bubble about what it's alerting you to, i.e. `Action needed` or `Permission needed` or `Another session needs your input`.