It might not work since they’re different platforms with different APIs. The only way an app might work on both platforms is if the app itself chooses to support both APIs.
That said, there’s a level of interaction between the two since they both use ActivityPub. I.e. on Mastodon I can search for a particular Lemmy user and see their posts.
Open the Chrome menu, go to Settings > Site Settings > All Sites. Check if you have Tiktok in there, click the site and you’ll see a Clear & reset button. Clicking the button should remove any notifications from the site coming from Chrome.