[Bug]: Extensions doesn't work in the browser sidebar

[ICaPiCo]

Pre-Submission Checklist

• [x] I have checked the existing/closed issues to ensure this issue has not already been reported.
• [x] I am using the latest supported version of the browser.
• [x] I have tried disabling all browser extensions/add-ons to rule out interference from these.
• [x] I have tried clearing the browser cache and cookies.
• [x] I have checked with a new profile and the issue still occurs.
• [x] I have provided detailed step-by-step instructions on how to reproduce the issue.
• [ ] I have included relevant screenshots or console outputs.
• [ ] I have checked that this problem is not occurring in the latest version of Firefox ESR.
• [ ] This issue is specific to this browser and does not occur in other browsers.

Bug Summary

Simple bug: All of the "tabs" in the browser sidebar don't use the installed extensions.

Reproduction Steps

1. Install an extension that modify a certain or multiple website.
2. Add this website as a web panel.

Expected Behavior

Extension activating and actively working in those web panels

Actual Behavior

Extensions not working

Screenshots

Sidebar I'm talking about (the one at the right):

Browser Version

Version 11.23.1 (64-bit) | Firefox: 128.8.0

Operating System

Windows 11

Additional Context

No response