You don't have to store the fingerprint for this. You can simply store a model, that only gives a positive result for the correct fingerprint. This is similar to how people don't store passwords, they store a function that can verify the password.
I can't speak for how your laptop in particular implements this. Maybe their programmers suck and they really do store the fingerprints. That would make your concern valid. But generally that is not how a normal developer would set up fingerprint verification - it's well known that you shouldn't store the fingerprint.
Furthermore, there are usually laws about storing biometric data specifically. These can be more strict than even storing passwords. So if you're worried about giving up your fingerprint data, you should look into those for your jurisdiction.
As for: Is there a way someone who isn't you could get past the fingerprint reader? Yes, of course. No security is perfect.
- They could get your fingerprint and make a fake finger of their own
- They could somehow force or trick you into pressing you finger on the reader
- They could find a bug in the software/hardware and get past without providing the right print
Also, there are risks as well: You could lose the finger (in an accident) and be unable to unlock it yourself. The software they use may be bad and fail to recognize your fingerprint even though it's correct.
But similar things also apply to similar systems, like passwords or keycards. So fingerprints are not particularly better or worse than the alternatives. Unless perhaps you work in a factory that has horrible OSHA compliance.
Regarding your concern about learning the details of how the hardware/software works, welcome to the problems of proprietary tech. If the software was FOSS and the hardware was open (schematics available) that would not be a problem. However, making things proprietary can make the company more money, so it's harder to find FOSS alternatives because the proprietary vendors have more money to spend on marketing and development. You should still look for FOSS options if you care.