How can I make my master's thesis more widely accessible online?
arXiv is the de facto way of publishing papers online. Considering that arXiv allows publishing theses as well (see Is it advisable to upload theses to the arXiv?), I would consider arXiv a good option for long-term public storage of your thesis.

However, you have to be aware of certain things.

Firstly, things posted to arXiv are public forever. This means you cannot remove your thesis from there once it is published. I would consider this to be the case for all information posted to the Internet (it is theoretically possible someone has a copy), but it may be the case that nobody is interested enough in your thesis to have a copy.

Secondly, your must be aware of your university policy. Some universities may not allow posting your thesis online. However, I wouldn't choose to attend such a university if I had a choice.

Thirdly, arXiv requires you to post the full LaTeX source code if your thesis is made in LaTeX. This means all of your university's LaTeX style files that may be copyrighted by your university need to be posted too.

Fourthly, arXiv covers only some fields. I was lucky to have my thesis in the field that arXiv covers. If your thesis isn't within arXiv's scope, you have to find a suitable repository from elsewhere.

I'm not sure if the LaTeX source requirement is valid anymore, but it was valid when I posted my thesis in 2014. I actually just was lazy and didn't check with the university if posting the university's .sty files is permitted. I don't expect to be sued because of this. With some amount of work, you could eliminate the use of your university's .sty files, but then the thesis wouldn't look like a thesis made in your university.