TSM seems to be pretty dead in terms of development and bug fixes ... no check-ins Oct 2021 till today March 2022.
Bundling information into session management doesn't seem to be a possibility unless I was to fork the project for myself.
Another option might be to store either the individual sites or domains that should be locked by default. (Would remove need for session management and move to more of a generic implementation)
Would need to be able to store all of this and be able to add\remove via tabs AND in the configuration.
Challenge would be for links to be either too specific (may not work on tabs on a restore) or too generic (too many tabs on restore would be locked)