Hi Flyboy.
I do not know but would hazard a guess from what you are saying that the printer is perhaps aware of a dry print head rather than empty cartridges. At the risk of suggesting something you have already tried, you might want to experiment with one of the hardware / firmware resets available to you.
To get to the hidden menu on your model:-
Turn off the printer, wait 10 seconds, power it back on -
as soon as the printer starts to power up, press the
<BACK< button on the front panel four times.
You should now have the support / reset menu appear!
There will be various options which may be of interest, among them is the reset menu. My suggestion would be to try a "partial reset" first which will keep some of your settings etc - but will reset some internal errors (though of course they will be reestablished if there really is a problem).
If this doesn't work, you can try the "semi-full" reset which will clear ALL custom settings and will take the printer to almost a factory default setting - and again should clear out internal error flags.
The last ditch attempt is the "Full Reset" and (I think) is a combination of the reset above PLUS (and I may be wrong
but I know if you lose power you can "brick" your machine) I think it tries to reload the firmware from (presumably) a backup.
I would be tempted to try the first two resets only at this stage - if you can remove the printhead easily it might be worth seeing if it seems "dry" or "wet" which may give you a clue as to what might be going on. This link might offer some useful guidance on checking and cleaning your print head further and it may be that once it has been given a rinse and a reset, things start to co-operate again.
https://www.bchtechnologies.com/blog/how-to-clean-hp-950-933-printhead-officejet-8600-8610-8100-8620
The following may not apply to you - but as it is the same family of printers it just might be of use.
Also, I know from personal experience that with the HP OfficeJet 7000 (a very different printer but still HP and still with quirks), If any ink has leaked from a cartridge for any reason, it tends to somehow get between the printhead contacts and the printhead holder contacts - generating an assortment of flashing LEDs on my printer - and possibly rather more useful messages on yours.
Ditto, on the OJ 7000, ink can ALSO drip down and cause problems on the PCB which connects the printer to the ink cartridge chips. In this case, I find the easiest way to solve the problem, is power off, cartridges out, printhead out, clean all contact with isopropyl alcohol and a GENTLY wipe from a lint free cloth and then (with my printer at least), squirt IPA from a syringe into the BASE of the cartridge holder until clear IPA comes out and not the spilled ink. This may NOT be an issue on your printer - but if there IS some ink on the PCB or on the contacts between printhead and holder and/or ink cartridges and holder, then this too can generate a variety of errors.
You may want some kitchen roll on the paper out tray (and take the paper stack out first)
Even more aggravating is that the contact method of "raised bumps" is really not that brilliant from a reliability point of view - and around half the time, simply "re-seating" the printhead and/or cartridges (even without a clean) makes it work again. In my opinion it's quite a poor design which even used to fail with OEM cartirdges from time to time.
Let us know how you get on and if I can find any more info I will bung you a note.