Both the Gem of the Earth and the Endersurge Gem do not work on the spectrum workstaffs. I conducted a test on AOF7 with three pickaxes, a diamond pickaxe with fortune 6, a diamond pickaxe with fortune 6 and the gem of the earth and the endersurge gem, and a spectrum workstaff with fortune 6 and both gems. The results were that the ore mined from the diamond pickaxe with both gems was significantly higher than the other two, which were at similar levels. The test can be found here: http://cds.vahin.dev/u/99c2f87e-9dbf-426c-883a-b27dbe59c252.mp4. The three pickaxes also will be attached. There is a difference of 5 items between the first and Third, with the third having 5 more. The second chest has 600 more ores than the first.

It shouldn't matter, as the +4 to sharpness gem doesn't do anything either.

Given the loot category system isn't designed with multitools in mind, I imagine dedicated compat would need to be written for everything to work as expected.

Do the gems at least work if you override the loot category to pickaxe in adventure.cfg?

Is the +4 levels of Sharpness instead of Fortune on the Malachite Workstaff somehow related?

Hmm I didn't notice that, but even then the workstaff chest should still have more than 5 more items from breaking 3 stacks of coal ore. 2 extra levels of fortune should still count for something.

Thanks for telling me, I tested it with sharpness and there was no difference in the damage. The test can be found here.
The two workstaffs I used were:

I think the cause of the issue is that the Spectrum Workstaffs seem to have the "zenith:enchant_level_modifier_blacklist" tag, but still allow for gems that modify the enchant levels to be added.