If you're using the latest version of Edge Chromium on both Canary and Dev channel, then the company has introduced a mute button in the PiP Mode.
Here' how you can enable it:
Copy-Paste following flag address and hit enter
Change settings from Disabled to Enabled.
Now if you launch PiP Mode in Edge browser, and hover the cursor over PiP Mode window, you will notice a mute icon available on the bottom left corner.
Check following screenshot:
Thank you for this information. I'm sure it will be useful for many of our users that might not have been aware.