Center the mouse cursor at startup

When I open a session, the mouse cursor moves at the bottom-right of the screen, at a fixed position. The coordinates are about (x:1730, y:970) on a 1920x1080 screen.

When I close the session, the mouse goes again to this position.

I am not sure if the issue really comes from mutter, or gdm, or other component.

This behavior is specially annoying because your first action after log-in will probably consist in launching an application by clicking its icon at opposite position of the screen, in the top-left part of the launch bar.

ProblemType: Bug
DistroRelease: Ubuntu 20.04
Package: mutter 3.36.1-3ubuntu3
ProcVersionSignature: Ubuntu 5.4.0-24.28-generic 5.4.30
Uname: Linux 5.4.0-24-generic x86_64
ApportVersion: 2.20.11-0ubuntu27
Architecture: amd64
CasperMD5CheckResult: skip
CurrentDesktop: ubuntu:GNOME
Date: Sun Apr 19 09:03:01 2020
InstallationDate: Installed on 2018-04-07 (742 days ago)
InstallationMedia: Ubuntu 18.04 LTS "Bionic Beaver" - Alpha amd64 (20180403)
ProcEnviron:
 TERM=xterm-256color
 PATH=(custom, no user)
 XDG_RUNTIME_DIR=<set>
 LANG=fr_FR.UTF-8
 SHELL=/bin/bash
SourcePackage: mutter
UpgradeStatus: Upgraded to focal on 2020-04-04 (14 days ago)