Devtools tab of extension doesn't load properly in Firefox private mode

Bug Description

I found an issue with a Firefox extension. Even though the extension is allowed to run in private windows, the LiveDebugger DevTools side panel remains empty when opened in a private window.

Actual Behavior

Blank page in LiveDebugger DevTools window.

Expected Behavior

I expected it to work the same as in normal browsing mode, just like in other browsers such as Brave.

Steps to Reproduce

Allow this extension in private mode and open LiveDebugger DevTools side panel on your application site.

Elixir version with Erlang/OTP

Erlang/OTP 28 [erts-16.0] [source] [64-bit] [smp:8:8] [ds:8:8:10] [async-threads:1] [jit] [dtrace] Elixir 1.18.4 (compiled with Erlang/OTP 27)

LiveDebugger version

live_debugger 0.3.0 (Hex package) (mix) locked at 0.3.0 (live_debugger) afd8c013 ok

Phoenix version

phoenix 1.7.21 (Hex package) (mix) locked at 1.7.21 (phoenix) 336dce4f ok

Phoenix LiveView version

phoenix_live_view 1.0.17 (Hex package) (mix) locked at 1.0.17 (phoenix_live_view) a4ca05c1 ok

Operating system

macOS Sequoia 15.5

Browser(s)

Firefox 141.0.3