I recently bought a perfectly working Mamiya 528AL

The rest of your post directly contradicts this. If where you got the camera from declared it as in mint or great condition, you may want to return it if it is, in fact, not perfectly working.

But, before we get there...

The rewind mechanism is essential. It disengages the film advance so that you can get the film off of the take-up spool and back into the can.

If the button were stuck in, you would still be able to cock the shutter, but the film would not advance, and you'd end up with a double exposure (or more).

However, you state:

But the rewind release button was stuck (and still is)

That statement combined with:

half of it was tangled in the take-up spool,

leads me to believe that the film was incorrectly loaded onto the take-up spool or hopped off through a possible really hard or fast crank on the cocking lever.

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To conclude...you shouldn't have sticky liquid anywhere inside the film compartment. The rewind button needs to work. The problem in your last roll could have been due to you cranking the lever or something else entirely. You can try again with another roll and make sure to be easy on the lever to see if this problem occurs again. Though, not having the rewind button means you'll be exiting your film in a darkroom/change bag from here on out until it's fixed.

I recently had two cameras serviced (shutter times adjusted, full cleaning) for roughly ~$250 apiece. I'd expect to pay around that for someone to clean up your camera. This cost is obviously a lot more than the camera's value, so I don't know that I'd actually pay it. You'd be better served returning it and buying from a different seller. (Your camera isn't worth much, but the repairman's time is)