A fair number of gearcases use #0 NLGI grease. Typical stuff that you pump out of a grease gun is #2. Anyway its soft and nearly flowable and has a lot of oil while not being full on liquid.
The problem with #2 is it is thick enough to get smashed out of the way and then stay there where it does no good. A softer consistency is needed to get lube to the moving parts reliably while not presenting quite the sealability problem as the liquid.

Usually NLGI 0 or 1 is spec'd.
Unfortunately its usually too-expensive/impractical-to-buy/hard-to-source the OEM goo for the average joe.
In "slow" speed gearcases, such as your drill, i have used John Deere Corn Head Grease.
I can walk in the JD store and buy a tube for less than $4.
Its a high quality NLGI-0 and is polyurea based. It was designed to semi-liquefy in use, but remain semi-solid at rest, (for its intended application.)
Check it out here:
https://www.greenpartstore.com/John-Deere-Special-Purpose-Corn-Head-Gun-Grease-AN102562.html
Heres a cool video of it in action:
As always, advice has to be taken with a grain of salt. What works for one application may not be good for another.
And the thought of “if it aint broke, dont fix it” comes to mind. The existing factory grease will last a LONG time.
Unless its leaking, it might be best to leave it alone.
