gamemoderun enables gamemode, but doesn't register process

Starting a game with gamemode enables gamemode, but doesn't register the game process to use gamemode. This prevents things like core pinning (I use a 7950X3D) from working.

I'm on Fedora 39 with the most up-to-date version of the Steam Flatpak from flathub.org, but I manually installed version 1.8.1 of Feral gamemode (Fedora 39 ships with 1.7, which doesn't support core pinning). Running `gamemoded -t` returns `: All Tests Passed!`. Launching for example `gfxgears` with `gamemoderun gfxgears` successfully activates gamemode and registers the process:

```
> gamemoded -s79042
gamemode is active and [79042] registered
```

Querying a game running via the Steam Flatpak returns this:

```
> gamemoded -s77895
gamemode is active but [77895] not registered
```

And as I said, core pinning doesn't work. When I manually register a running process using `gamemoded -r77895`, it works properly including core pinning, but I have to do this manually every time after launching the game.

Exiting the game properly disables gamemode if it was the only gamemode process active, so it does _something_, it just doesn't register the process properly.

I set the "Launch Options" in Steam to:

```
gamemoderun %command%
```

Tested with Baldur's Gate 3 (including `--skip-launcher`), PlateUp! and Valheim (both Proton and native Linux version) so far. None of them are registered.

Running the Steam Flatpak with `flatpak run --log-session-bus com.valvesoftware.Steam` shows that the `org.freedesktop.portal.GameMode` portal is called. This is the output after a simple session where I started Steam, then Valheim:

```
[...]
/bin/sh\0-c\0gamemoderun /home/bird/.var/app/com.valvesoftware.Steam/.local/share/Steam/ubuntu12_32/reaper SteamLaunch AppId=892970 -- /home/bird/.var/app/com.valvesoftware.Steam/.local/share/Steam/ubuntu12_32/steam-launch-wrapper -- '/home/bird/.var/app/com.valvesoftware.Steam/.local/share/Steam/steamapps/common/SteamLinuxRuntime_sniper'/_v2-entry-point --verb=waitforexitandrun -- '/home/bird/.var/app/com.valvesoftware.Steam/.local/share/Steam/compatibilitytools.d/GE-Proton8-32'/proton waitforexitandrun '/home/bird/.var/app/com.valvesoftware.Steam/.local/share/Steam/steamapps/common/Valheim/valheim.exe' -force-vulkan\0
[...]
C29: -> org.freedesktop.portal.Desktop call org.freedesktop.portal.GameMode.RegisterGameByPIDFd at /org/freedesktop/portal/desktop
B6170: <- :1.24 return from C29
B-1: <- org.freedesktop.DBus signal org.freedesktop.DBus.NameOwnerChanged at /org/freedesktop/DBus
B-1: <- org.freedesktop.DBus signal org.freedesktop.DBus.NameOwnerChanged at /org/freedesktop/DBus
ERROR: ld.so: object '/home/bird/.var/app/com.valvesoftware.Steam/.local/share/Steam/ubuntu12_64/gameoverlayrenderer.so' from LD_PRELOAD cannot be preloaded (wrong ELF class: ELFCLASS64): ignored.
[...]
C29: -> org.freedesktop.portal.Desktop call org.freedesktop.portal.GameMode.RegisterGameByPIDFd at /org/freedesktop/portal/desktop
B6174: <- :1.24 return from C29
gamemodeauto:
ERROR: ld.so: object '/home/bird/.var/app/com.valvesoftware.Steam/.local/share/Steam/ubuntu12_32/gameoverlayrenderer.so' from LD_PRELOAD cannot be preloaded (wrong ELF class: ELFCLASS32): ignored.
[...]
C29: -> org.freedesktop.portal.Desktop call org.freedesktop.portal.GameMode.RegisterGameByPIDFd at /org/freedesktop/portal/desktop
B6178: <- :1.24 return from C29
B-1: <- org.freedesktop.DBus signal org.freedesktop.DBus.NameOwnerChanged at /org/freedesktop/DBus
B-1: <- org.freedesktop.DBus signal org.freedesktop.DBus.NameOwnerChanged at /org/freedesktop/DBus
ERROR: ld.so: object '/home/bird/.var/app/com.valvesoftware.Steam/.local/share/Steam/ubuntu12_32/gameoverlayrenderer.so' from LD_PRELOAD cannot be preloaded (wrong ELF class: ELFCLASS32): ignored.
[...]
C29: -> org.freedesktop.portal.Desktop call org.freedesktop.portal.GameMode.RegisterGameByPIDFd at /org/freedesktop/portal/desktop
B6182: <- :1.24 return from C29
gamemodeauto:
ERROR: ld.so: object '/home/bird/.var/app/com.valvesoftware.Steam/.local/share/Steam/ubuntu12_32/gameoverlayrenderer.so' from LD_PRELOAD cannot be preloaded (wrong ELF class: ELFCLASS32): ignored.
[...]
C29: -> org.freedesktop.portal.Desktop call org.freedesktop.portal.GameMode.RegisterGameByPIDFd at /org/freedesktop/portal/desktop
B-1: <- org.freedesktop.DBus return from C19
[...]
C29: -> org.freedesktop.portal.Desktop call org.freedesktop.portal.GameMode.RegisterGameByPIDFd at /org/freedesktop/portal/desktop
B6193: <- :1.24 return from C29
C30: -> org.freedesktop.portal.Desktop call org.freedesktop.portal.GameMode.UnregisterGameByPIDFd at /org/freedesktop/portal/desktop
B6196: <- :1.24 return from C30
[...]
C29: -> org.freedesktop.portal.Desktop call org.freedesktop.portal.GameMode.RegisterGameByPIDFd at /org/freedesktop/portal/desktop
B6200: <- :1.24 return from C29
C30: -> org.freedesktop.portal.Desktop call org.freedesktop.portal.GameMode.UnregisterGameByPIDFd at /org/freedesktop/portal/desktop
B6203: <- :1.24 return from C30
[...]
```

Running `gamemoderun` inside the Flatpak via `flatpak enter com.valvesoftware.Steam sh` properly registers the process that is run (I tested it with `top` even though that doesn't make sense for gamemode).

Any idea what could cause this not to work?

Reproduce with Steam Flatpak using the Launch Option `gamemoderun %command%`, then compare `gamemoded -s` with a direct `gamemoderun` invocation inside the Flatpak. Inspect the `flatpak run --log-session-bus` output for GameMode portal registration and confirm done when the launched game process is registered and core pinning works without manual `gamemoded -r`.

Written by the indexing model from the issue text.