Technically Impossible

Lets look at the weak link in your statement. Anything "Technically Impossible" basically means we haven't figured out how yet.

Japanese input on Clear Linux with Mozc via Ubuntu container with Distrobox


Abstract

Although major Linux distribution as Ubuntu provides language input method as Mozc and user can use it out of the box, some distribution as Clear Linux doesn't. Typical solution for such exceptional distribution is to build own binary.

Distrobox will be rational solution to improve this situation. Distrobox gives some leverage to minor distribution with major distribution's container.
Example, exceptional distribution hosts major distribution's container. Installing language input method to container, then Distrobox provides it to the host transparently.

This post introduces how to provide Japanese input capability to Clear Linux with Mozc on Ubuntu container through Distrobox.
Although Clear Linux works as container host in this post, concept of solution here will work commonly for other distribution.

Assumption and Resources

version
Clear Linux Desktop*1 36420
Distrobox*2 1.3.0
Ubuntu container*3 22.04

Preparation

Update catch-up of Clear Linux
swupd check-update
sudo swupd update
Docker installation and configuration

Install Docker and make it runnable without reboot.

sudo swupd bundle-add containers-basic
sudo systemctl enable --now docker

To run Docker without root, add current user to "docker" group and makes it effective immediately.

sudo usermod -aG docker $USER
exec su -l $USER

Due to stateless concept *4, Clear Linux doesn't have "/etc/hosts". This command is to supplement it.

sudo touch /etc/hosts

Distrobox

Installation

Install Distrobox following the official guidance*5. In the case of this post,

curl -s https://raw.githubusercontent.com/89luca89/distrobox/main/install | sudo sh

Although the next command is not required this time, don't forget to register its path in the case to install to a custom directory. This is for the case installed to to "~/.local/bin".

PATH=$PATH:~/.local/bin
Ubuntu container

Pull Docker image with Distrobox command. The next command is for

Docker image Ubuntu 22.04
Name of container ubuntu
distrobox create --image docker.io/library/ubuntu:22.04 --name ubuntu

Distrobox currently support following distributions*6. User can pick favorite one.

Then, enter the container.

distrobox-enter ubuntu
Mozc on Ubuntu and IBus

Be careful. In this section, run all commands on container, not on host.

At first, catch-up updates.

sudo apt update -y
sudo apt upgrade -y

Install mozc packages and related one.

sudo apt install ibus-mozc mozc-data mozc-server mozc-utils-gui -y
sudo apt install libcanberra-gtk* -y
IBus configuration from Ubuntu

Then, start IBus configuration on Ubuntu.

ibus-setup

From here, follow step-by-step in GUI as following screenshots show. If the list of ibus-setup doesn't include Mozc, try next command.

ibus restart
ibus-setup

Screenshot: step-by-step on Ubuntu

After adding Mozc, back to desktop on host.

Settings on Clear Linux

Be careful. In this section, do all operation on host, not on container.
Now, Settings of Clear Linux can see Mozc on Ubuntu. Open settings and follow

Settings > Keyboard > Input Sources

Adding Mozc on Host, then taskbar shows input method as screenshots indicate. Japanese input with Mozc on Clear Linux finally works.

Screenshot: Mozc on Clear Linux

Daily use after rebooting

Although both host and container keep configuration of Input Sources above after reboot, it doesn't work on host without Ubuntu container. Run the next command on host just after booting. It would be better to add it at the end of ".profile".

distrobox enter ubuntu -- bash -l -c '"ibus-daemon -drx"'

Screenshot: Mozc on Clear Linux