The optics of this is not aiming at Japan.
At this time, China got what it needs to glass Japan from Hokkaido at the north right down to Kyushu to the south and still has what required to make Americans live out Fallout 76 for real.
This is in response to US Navy doing "Pirates of the Caribbean", seizing oil tankers outbound from Venezuela.
A proper "demonstration" would be an ocean-going Panamax participate in combat operation, either demonstrating "sustained fire support" with its full deck of VLS land attack cruise missiles, or full-on "Alpha Strike" in fashion only the once-envisioned arsenal ship could pull off.
That would be playing a good hand badly.
These modules are not magic, and cargo ships converted with them will not be a match for a proper warship of comparable tech levels.
What these modules does is it allows the PLAN to rapidly spin up potentially ridiculous numbers of combat auxiliaries that can multiply the combat capabilities of a PLAN fleet.
But even such a new combined fleet will be fighting against the odds trying to take on the U.S. in the Caribbean as the opening move of a direct superpower clash.
The Caribbean is America’s backyard, and trying to take on the US head on in a direct clash there would be as unwise as the US trying to fight to hold the Taiwan Strait from China.
Your other ‘demonstration’ examples defeat the whole purpose of the demonstration part as you are basically jumping straight into launching a new war.
That is one possible use of such ships, but firstly, China is clearly trying to avert a war, not trigger it. Secondly, if you wanted to do a surprise alpha strike, you will want to keep this capability under the most heavy of guard to make sure you can achieve the surprise part. Openly showing them off in from of a park is the last thing you will be doing if that was the case.