OK on the mechanics.
I'd avoid anything like your first link, low voltage and small output shaft. The power will not be that high and the life under load rather short.
The second is more practical, just with a different gearbox ratio to give a reasonable speed at the drill bit.
I'd also only use 24V ones, they should be more efficient and give better results; higher voltage means lower current for the same power.
This is the nearest I can find so far; for an inline-style one:
**broken link removed**
That has has a 10:1 gearbox which gives ten times the torque of the bare motor but still gives a drill speed of up to 1000RPM.
Or better still, a right-angle one with a bigger [and better made looking, machined rather than pressed] motor, still less than 50mm wide.
**broken link removed**
The 24V 470RPM version of that should work well. The fact that they have an 8mm output shaft (hopefully) shows they are designed for serious loads rather than just being toy motors..
It looks like there are a few places selling those, or get them direct from aliexpress etc.
I'd add a small thrust bearing for the chuck to seat against, so the drilling force is applied to the gearbox body rather than just the output shaft, they should last a lot longer that way.
eg.
https://www.ebay.co.uk/itm/BEARING-...748314?hash=item2edee077da:g:i4MAAOSw-RRXCny4