Installing fcitx and fcitx-googlepinyin in one row and restarting causes failure to log into desktop GUI

[FishBone E.K.]

# How to reproduce the bug:
sudo apt install fcitx fcitx-googlepinyin
Switch keyboard input method system to Fcitx 4 in Language Support
Restart

# Bug symptom
After entering password in the login screen, the desktop doesn't pop up.
Instead, the screen turns into the boot splash (on my laptop it's a big Lenovo icon at the middle and Ubuntu icon at the bottom), with a mouse cursor that I can move around. And I'm not able to start a terminal (Ctrl+Alt+T), etc.
If I switch to other tty (for example, tty4) and kills the first tty, the login screen shows up. After entering the password, it's not boot splash but the graphic of tty4 as the static background (the tty cursor doesn't blink, that is), and still with a mouse that I can move.

By the way, this symptom won't happen 1) if I install fcitx without installing fcitx-googlepinyin at first, and switch keyboard IM system to Fcitx 4, restart, then install fcitx-googlepinyin, 2) or if I install fcitx only.
And I noticed that there's some log entries in my journal
Mar 14 10:57:55 yep systemd[1503]: <email address hidden>: Failed with result 'timeout'.
Mar 14 10:57:55 yep systemd[1503]: Failed to start GNOME Shell on X11.
But around those entries I didn't find any other log entries indicating possible reason of 'timeout'.

# The way I solved this problem
Purging fcitx and fcitx-googlepinyin and restarting makes my ubuntu works fine again.

Sorry for my bad Eng skill.
And thanks for your contribution to Ubuntu and free software!

Ubuntu 22.10
fcitx 1:4.2.9.9-1
fcitx-googlepinyin 0.1.6-5

ProblemType: Bug
DistroRelease: Ubuntu 22.10
Package: fcitx-googlepinyin (not installed)
ProcVersionSignature: Ubuntu 5.19.0-35.36-generic 5.19.17
Uname: Linux 5.19.0-35-generic x86_64
NonfreeKernelModules: nvidia_modeset nvidia
ApportVersion: 2.23.1-0ubuntu3
Architecture: amd64
CasperMD5CheckResult: unknown
CurrentDesktop: ubuntu:GNOME
Date: Tue Mar 14 13:11:23 2023
InstallationDate: Installed on 2022-02-18 (388 days ago)
InstallationMedia: Ubuntu 20.04.3 LTS "Focal Fossa" - Release amd64 (20210819)
SourcePackage: fcitx-googlepinyin
UpgradeStatus: Upgraded to kinetic on 2023-03-10 (3 days ago)