Step debugging not working in VS Code versions after 1.103

Describe the bug
I am developing an extension for VS Code called Mentor (Repository). It is primarily developed in TypeScript and built as a web extension so it can also run in browser based environments using esbuild.

Since VS Code version 1.104 I cannot step debug the extension anymore. Versions prior to 1.103 work. The debugger stops at breakpoints, however, but then I cannot see any bound variables and the step debugging functions / buttons / keys are not responsive. The step debugging controls in the Developer Tools of the debugged VS Code instance is working but quite cumbersome.

The debugger is basically frozen. I am primarily using Ubuntu 24.04 for developing but I can also reproduce the issue on my Mac. When I install VS Code 1.103 everything is fine and when switching to 1.104 the debugger is broken.

To Reproduce
Steps to reproduce the behavior:

1. Clone the Mentor (Repository) repository.
2. Set a breakpoint (example: extension.ts / activate function)
3. Try to use the step debugging controls

Log File
Will try to provide this later.

VS Code Version:
1.103 / 1.104

Additional context
Add any other context about the problem here.