If the Professor who recommends me somewhere has coauthored papers with professors there, would the LORs hold tremendous value?
In my view (and I was MSc admissions officer at some point) recommendation letters at MSc level are largely a tick box exercise. I have admitted more than hundred MSc students and a recommendation letter hasn't made a difference even once. It is fine from my point of view that the student shows they can find somebody professional to recommend them, but as long as such a letter is not actively damaging, the box is then ticked and it doesn't make much more of a difference. Obviously I can't speak for all places.
This makes sense as well; applicants shouldn't have an advantage if they know somebody who published with me or XXX from our institution. Generally admitting students is not about whom they know but how good they are, and because 99% of recommendation letters are positive, I have to assume that there's very little information in them about the quality of the student. Even if some read a little bit less positive, this may be because the writer has a more critical attitude to recommendation letters, rather than the student being bad. People who write glowing recommendation letters for everyone who asks are around all over the place. Also recommendation letters at this level are quite regularly written by people who don't know more about the student than their set of results and maybe that they asked a few questions in class, but maybe not even that (at PhD level this is a bit different). Previous marks and course choices should totally dominate what's in recommendation letters. I'd go so far and say I'd be wary of institutions where this is different.