Considering withdrawal from part-time Masters Degree to focus on a new job

I should point out that I already have a level 8 undergraduate degree in Computer Science from back when I was a full-time student. It has proven useful for qualifying for interviews but I have never seen a level 9 listed on anything other than desirable criteria.
 
The most relevant advice you are going to get will be from your new colleagues and management, maybe discuss with some of those if you can find some colleagues that like to mentor new staff.

Internal promotion is often used as a carrot to get people to do a checklist of tasks or roles that are otherwise hard to get people to do, in every department that game is likely to have its differences.
 
You may never see it either, but assuming you see the sky as your limit eventually everyone else going for the jobs you are will have masters in something or other. It may seem hard now but doing one later with potentially a more time consuming job and family is even harder.

It’s pretty simple really, if you can manage it get through it now with the minimum effort you can, as it’ll be very hard to go back.
 
  1. You are only a few months into the course and are finding it stressful
  2. You don't have time to do it.
  3. You have already landed a job in the field that you want
I wouldn't do it...but I would check with your new boss was doing the Masters a reason for getting the job in the first place. You don't want to put future promotions in jeopardy by dropping out if your boss thought it was important.

I did a Grad Dip in Financial Planning. Another 2 modules and I would get a Masters. I was starting up my company at that time and was getting very busy. I couldn't see what benefit doing those 2 modules would bring me besides having a Masters degree. So I didn't do it. Don't regret it for one second.