It doesn't have to be inkjet - color laser printers have been around for 20+ years just at a consumer level, and the Trek art department was far above consumer level. Also remember as the shows progressed the art department moved to digitally printing the backlit translite films in color. They clearly had access to good equipment, not just desktop inket printers
My bet is either on color laser transparencies or whatever unknown digital printing method they used for the later color translites (though on clear acetate). If this is DS9, we're looking at maybe 1996-1998, and if it's the Enterprise finale PADD, it's from 2005.
Here is a little demo screen made of a color laser transparency, backed with the previously mentioned brushed faux metal shelf liner:
Same here on the circuit graphics - color laser backed by brushed tape that is similar to but maybe a bit higher quality than the shelf liner (less adhesive mottling):
(the small screen and the inset buttons are about the same size)
You see similar color mottling in the larger areas, caused by the tape adhesive.
The metal printing is a very cool process, but... Even if it was available 11-20 years ago, I really really don't think they would do metal sublimation printing just for this one-off PADD's graphics when they were already doing the same effect with clear prints and faux metal/holographic tape.