So that is not correct workaround at all for AGPL licenses. By moving the MuPDF logic into a Web Worker, you are still providing a "modified version" of the program to the user to interact with. The "separation" via a Web Worker does not change the fact that the user is interacting with a system that includes AGPL-licensed code.
Exactly.
It is a clear AGPL license violation without contacting the MuPDF sales team.
If the OP doesn't want to contact the sales team, it should be open source.