Long story short: I a working on a printing project requiring me to print grid on non standard size of paper: like this
On one hand, using commercial/industrial printer looks overkill for me since my project is not yet large scale and on another hand, it just consists in drawing straight lines.
I have read about all those reverse engineered HP print-heads projects which seem dead by now (2022).
Eventually what would be recommended for such a project?
Ideally, is there any kind of inkjet pen that could be attached to a mobile part commanded by arduino?
The pen is a consumable item.
Providing you are using normal paper, the pens usually run out of ink before they physically wear down and become unusable.
It is a graph paper, just like papier millimétré in french on a lenghty roll of A5 paper that will be used for graphing data later.
The gird spacing would be millimeter.
I would take a look at this printer from Adafruit. These are easily interfaces to a microcontroller. They have a few of them including one that is just the guts so you can put it in your own enclosure.