Mouse is escaping monitor while playing splitgate -- include `gamescope`

**Game information**

Splitgate

**Distribution name and version where applicable**

```
cat /etc/os-release
NAME=Fedora
VERSION="Kinoite 34.20210817.0 (Silverblue)"
ID=fedora
VERSION_ID=34
VERSION_CODENAME=""
PLATFORM_ID="platform:f34"
PRETTY_NAME="Fedora Kinoite 34.20210817.0 (Silverblue)"
ANSI_COLOR="0;38;2;60;110;180"
LOGO=fedora-logo-icon
CPE_NAME="cpe:/o:fedoraproject:fedora:34"
HOME_URL="https://fedoraproject.org/"
DOCUMENTATION_URL="https://docs.fedoraproject.org/en-US/fedora-silverblue/"
SUPPORT_URL="https://fedoraproject.org/wiki/Communicating_and_getting_help"
BUG_REPORT_URL="https://bugzilla.redhat.com/"
REDHAT_BUGZILLA_PRODUCT="Fedora"
REDHAT_BUGZILLA_PRODUCT_VERSION=34
REDHAT_SUPPORT_PRODUCT="Fedora"
REDHAT_SUPPORT_PRODUCT_VERSION=34
PRIVACY_POLICY_URL="https://fedoraproject.org/wiki/Legal:PrivacyPolicy"
VARIANT="Silverblue"
VARIANT_ID=silverblue
OSTREE_VERSION='Kinoite 34.20210817.0'
```

**Flatpak info**

```
Flatpak 1.10.2
```
```
flatpak --gl-drivers
default
host
```
**Problem description**

**Does this issue reproduce with native Steam**

Most likely yes

In the game splitgate the mouse is escaping the game while in full screen. A well known work around is to use gamescope(https://github.com/Plagman/gamescope) would it bennifical to include this in the steam flatpak?

No source file, test, or entry point is named. Start by examining the Steam Flatpak packaging and how gamescope could be integrated, then reproduce Splitgate's fullscreen mouse escape; done would require an agreed integration approach and verification that the mouse remains contained.

Written by the indexing model from the issue text.