Hello, I reported this in ubuntu and was directed upstream (here).
I ran reportbug -B debian -q ibus-mozc in my ubuntu system, hence the
packages being ubuntu ones.

This is not a bug, but a default configuration issue in
/usr/share/ibus/components/mozc.xml

The initial ubuntu bug report is available at
https://bugs.launchpad.net/ubuntu/+source/mozc/+bug/1958492

The summary is:

/usr/share/ibus/components/mozc.xml has <layout> configured as "default"
instead of "jp".
This leads to the following behaviour:

1) Switching to "Japanese (Mozc)" just enables Mozc and doesn't switch to
the Japanese keyboard layout
but keeps the currently used one (whatever that may be).
Switching to Japanese (no mozc) DOES switch to a japanese keyboard layout
(ie: runs setxkbmap jp)
Why does a keyboard layout named "Japanese" NOT change to a japanese layout?
What's the rationale behind this?

2) The /usr/share/ibus/component/mozc.xml layout set to "default" leads to
very inconsistent behaviour.
Should I have 4 different layouts besides "Japanese (Mozc)", switching to
"Japanese (Mozc)" has four
possible different behaviors depending on the previously used keyboard
layout.
Very inconsistent.

This debian bug report is the very example of that:
https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=953046

3) Japanese users don't notice because switching from Japanese (without
mozc) to Japanese (Mozc)
just "works". (By chance, should they have another keyboard layout too,
they would experience the
inconsistencies pointed out in 2)

4) Non-japanese users (that usually don't have the Japanese (no mozc))
layout end up being unable
to switch input modes from the keyboard with the zenkaku/hankaku key (the
key to the left of the 1,
~ tilde in the us keyboard layout) because that doesn't exist in other
layouts.

A lot of information on the internet suggests changing the input mode to
hiragana from the menus,
but this is a workaround.
Changing to a japanese keyboard layout SHOULD let me change input modes
with the japanese keyboard
layout key explicitly designed to do so.