Printer driver (help for a friend..)

I managed to update a very old HP laptop of a friend to Win 10 thanks to the good people and threads on this forum. He's a mechanic and used to use it with Vista. The problem now is that I can't get an old HP printer installed. He sometimes prints some stuff to help when fixing some stuff...
The printer is an HP PSC 2355. This is compatible with the drivers for the PSC 2350 series from what I found. The HP's website only information regarding drivers says to install the built in drivers of the operating system. I searched for many hours and found out that the latest windows 10 installation media doesn't include drivers, they're included with WU. However WU doesn't find anything (yes, I followed the procedure in various ways, including device manager... never finds any printer...). What strikes me as odd is that another friend has Windows 10 built in drivers working with that, admittedly very old printer. The only difference is that he is runing x64 win10, whereas this old HP laptop is running x86.
Has HP asked M$ to stop including drivers for old printers or I am missing something ?
Could it be that the x86 version of Win10 doesn't have the same built in drivers ? But this printer is really old, it should have it, infact the whole "Add printer" Wizard is very strangely unpopulated with almost no printers at all. Could this be because of the original media I chose to install from ? But shouldn't WU find the printer anyway ?

Is there any way to check if there is an x86 driver for the printer ? I checked the WU repository but the results it gives don't have that printer...

 

By the way, the printer is recognized in device manager, but it's reported as having no controlers... (yellow mark or whatever..., as as the control panel printer list, it shows up but says it's got no controler.).

I also found a post on this forum, from someone that had to reinstall win10 with different base version to have his printer working, but it wasn't clear if it was caused by corrupt data or not...

 

Thanks a lot for your replies, I'll check it out after he opens the shop...
By the way, it's amazing that this printer is still on sale after all these years! I had no idea..