Garry's Mod x64 fails to load main menu/Chromium components

**Game information**
Garry's Mod [x64 version]

**Distribution name and version where applicable**
Ubuntu 23.10

**Flatpak info**
Flatpak 1.14.4
nvidia-545-29-06
default
host

**Problem description**
Upon launching the game, no main menu will appear and all Chromium components of the game fail to work. In the console: `No support for unprivileged usernamespaces. Loading Stub instead of Chromium...`

Relevant GH issue for Garry's Mod: https://github.com/Facepunch/garrysmod-issues/issues/5371

Relevant GH pull for flatpak that might solve this issue if implemented here: https://github.com/flatpak/flatpak/pull/3240

**Does this issue reproduce with native Steam**
No.

Start by reading the linked Garry's Mod issue and Flatpak pull request, then reproduce the missing main menu and Chromium components on the reported Ubuntu 23.10, Flatpak 1.14.4, and NVIDIA setup. Done means the x64 game loads its main menu and Chromium components under Flatpak without the reported unprivileged-user-namespace failure.

Written by the indexing model from the issue text.