Add Tab Sync Support for Sidekick Browser

[blacklightpy]

Describe the feature you'd like to request

Right now Tab Sync doesn't work for Sidekick Browser, because I think it stores session data in a different format than Chrome, with multiple sessions.

Describe the solution you'd like

Implement Tab Sync for Sidekick Browser.

Describe alternatives you've considered

Sidekick is working on their own sync since Google shut down the sync API, but still, it can then only sync with Sidekick. For cross-browser syncing I still need Floccus.