Gamescope disables steam overlay

**Description**
I have steam and gamescope as a flatpak but when games are launched with gamescope the steam overlay does not work and the built in FPS counter stops working. This would not be a big deal but, steam overlay seems necessary for steam input to work.

**Steps to reproduce**

1. Enable steam input on general settings and game properties
2. Enable steam input
3. Launch game
4. Get expected behaviour ( steam overlay, FPS counter, and controller support working)
5. Close game
6. Relaunch game with a gamescope command, for example gamescope -h 720 -H 1080 -f -- %command%
7. Steam overlay does not appear, cursor still appears, in some games it cant be moved, keyboard works as if it was in overlay (you can press esc or overlay shortcut again to get back to the game).

**Additional information**

System info
CPU: 7800X3D
GPU: 7900XT
OS: Arch with CachyOs repos
Desktop env: KDE Plasma 6.4 Wayland

I have 2 branches of gamescope installed up to date kernel and drivers

flatpak info com.valvesoftware.Steam

Steam - Launcher for the Steam software distribution service

ID: com.valvesoftware.Steam
Ref: app/com.valvesoftware.Steam/x86_64/stable
Arch: x86_64
Branch: stable
Version: 1.0.0.81
License: LicenseRef-proprietary
Origin: flathub
Collection: org.flathub.Stable
Installation: user
Installed: 43.8 MB
Runtime: org.freedesktop.Platform/x86_64/24.08
Sdk: org.freedesktop.Sdk/x86_64/24.08
Commit: c3c48d342c49c6c7d06f4b3db484e5133295415470522268dff753007fad37cc
Parent: e19b6cdee48b2c41e753f9abbe8e127b1f50f97547210c8da7771a51fcd96328
Subject: Fix mesa extra ref branch (28481f09)
Date: 2024-12-17 03:31:55 +0000

flatpak info org.freedesktop.Platform.VulkanLayer.gamescope/x86_64/23.08

gamescope - The micro-compositor formerly known as steamcompmgr

ID: org.freedesktop.Platform.VulkanLayer.gamescope
Ref: runtime/org.freedesktop.Platform.VulkanLayer.gamescope/x86_64/23.08
Arch: x86_64
Branch: 23.08
Version: 3.16.2
License: BSD-2-Clause
Origin: flathub
Collection: org.flathub.Stable
Installation: user
Installed: 119.2 MB
Commit: 1379b5ba7dff5164a302c6f3c338b65c4b3810cb47b07818f5527cf8684bed6d
Parent: 948bbbc0a0f0d7daf8a7d2fe9953ce7f6205e23cd5c5df4c6ffd631215884386
Subject: Update hwdata, libavif, gamescope, libinput and 3 more modules (24dd3793)
Date: 2025-03-02 16:17:52 +0000

flatpak info org.freedesktop.Platform.VulkanLayer.gamescope/x86_64/24.08

gamescope - The micro-compositor formerly known as steamcompmgr

ID: org.freedesktop.Platform.VulkanLayer.gamescope
Ref: runtime/org.freedesktop.Platform.VulkanLayer.gamescope/x86_64/24.08
Arch: x86_64
Branch: 24.08
Version: 3.16.4
License: BSD-2-Clause
Origin: flathub
Collection: org.flathub.Stable
Installation: user
Installed: 122.7 MB

Commit: 17e43683ae25c79ea78ab47e92aafaf8752dfd74037de8aba604435a3e98c2d8
Parent: 051868eeb5cc3737c22ba3728b80af544162da74e19dd8bbdf2cc6b49ecbf6a4
Subject: gamescope: Update gamescope.git to 3.16.4 (7a0b8a24)
Date: 2025-04-15 23:58:48 +0000

Start by reproducing the failure with the reported gamescope command and the listed Flatpak Steam and gamescope versions on Wayland. Compare Steam launched normally with Steam launched through gamescope, focusing on overlay visibility, the FPS counter, cursor behavior, and controller support. Done means these features work when games are launched with gamescope.

Written by the indexing model from the issue text.