> Would it help with better career opportunities?
It depends on the demand.
How many senior web devs are there? How many senior web dev positions are there?
Guestimate: 278057 senior developers and 23050 open positions [1].
How many distributed systems people are there? How many DS positions are there?
Guestimate: 1355 distributed systems people [1] and 219 open positions [2].
In other words: try to find some data that give some intuition. Sure, the 'research' (if you want to call it that, lol) is really biased but it probably is better data than your own intuition if you have no clue about it.
------- addressing some other stuff you said -------
Why do a masters in it? Do you want to research it as well? Writing a thesis is the obligatory part of it. At the Vrije Universiteit Amsterdam there is a masters in it that is spearheaded by Andrew Tanenbaum. But when you look at the courses, you see that many courses aren't about the theoretical part of distributed systems (see [3]).
To get your feet wet I'd recommend to fully follow distributed systems from Maarten van Steen. Why? First of all, his book [5] is being recommended by other people (see [6]). He also has lecture videos on it (from 2012, but since it's from a theoretical perspective they are still relevant). Edit: he deleted his videos, but I found one source here [4]. Oh yea, and he offers it all for free (which is also why I'm comfortable posting the new URL of the DS videos).
These are my 2 cents. Goodluck!
My personal opinion, don't pursue a masters. Just scan study guides of universities and figure out a curriculum, work less as a web deveoper but keep doing it (i.e. 4 or even 3 days per week) and study it independently.
[1] I searched it via LinkedIn by typing "senior web developer" and "web developer" and "distributed systems"
[2] I typed in "distributed systems" as job title on indeed.com. LinkedIn gave nonsensical results since everyone's course Distributed Systems was counted and almost no one had a title in it.
[3] https://www.vu.nl/en/study-guide/2018-2019/master/m-r/parall...
[4] https://u.cs.biu.ac.il/~ariel/download/ds590/videos/
[5] https://www.distributed-systems.net/index.php/books/distribu...
[6] https://teachyourselfcs.com/