Currently working as student part timer on a company that I really like.
When I'll finish my bachelor's degree, I will have been there for about 2-3 Years, additional to my 5 years working prior to that as a developer.

Today I learned, that our company doesn't usually pay the market price for devs (not a huge company, 150 employees, so it's understandable).
So now I don't know what to shoot for when discussing a raise after my degree. Should I still aim for market price? Should I argue with that and hope for the best?
I'm really unsure about that stuff...

Yes do that, you are there to earn too

Business is business. Your concern should be to negotiate a fair price. Make sure you actually know the market price for devs in your area, but even then they should pay what you're worth and you should hold them to that.

A lot of startups will take advantage of kids with no prior job experience who don't know what's fair and feel bad asking for compensation. But if you put in good work, and you don't get back good pay, that's you being screwed. Not them. Both sides should have some leverage in any discussion about compensation, especially for good, skilled work.

Is there a more reliable way to check the market value for devs in my area than to Google it?

I tried asking colleagues but they are dodging all the time and I didn't want to pressure them to tell me

You could try Glassdoor, but alas it is difficult.