As a software developer it is hard to believe that improving a piece of (proprietary) code can made it two orders of magnitude faster. Although parallelization can make it 2-5 times faster on a modern workstation of 6-8 cores, unless the original code was notoriously bad it is hard to imagine that it can really be faster by two orders of magnitude (~100 times faster) just by improvement, without changing the original algorithm. So, are you 100% sure that the acceleration you get is legit? Sometimes (especially with parallelization) when things are too good to be true, there is some subtle condition which usually breaks by parallelization. So, first make 100% sure (compare results produced for a wide range of input data) by the two versions of the software (the old and your version). I assume you use some version of version control system (who does not?), so you still have the old version somewhere. It does not matter if this experiment takes a few days - 1-2 weeks it has to be done to be 100% sure that something did not break and you do get identical results between the two versions of the software for a wide range of input data and not just by a small test case.
If you are 100% sure that you really improved the software without breaking anything, the main question is did you actually improved the original algorithm or not. Simply adding an OpenMP directive and parallelizing a code which was parallelizable all along, is not a publishable result. In this case, your improvements do not merit a publication and therefore no publication => no citation, since you did not create the original software. On the other hand, if you did more than refactoring / parallelizing the software and your contribution is significant you must publish these results on a technical-focused CS conference. Then everyone using your version of the software could cite this work and additionally could cite the online version of the software if it is publicly available.
On the legal version of your story, I really do not have the expertise to answer. In this case, I would search the IP policy of the university as @NateEldredge suggests and ask an experienced lawyer who knows about software patents. I do not think anyone of us here are really entitled here to give legal advice. Of course if your version of the software starts getting money for the university, you are probably entitled to a share and you must protect your rights as good as you can. It is just that right now, we do not know if this software is going to actually become a product for sale.
Also about your paragraph:
If I was working in industry this is about the time I'd be going to my
line manager and at asking for a salary bump or a promotion. In
academia it seems like this sort of work is relegated to a pat on the
back and a footnote. I suspect I'm being sour, but is this just the
way it goes?
I do not know how much experience you have in the software industry, but be rest assured that you do not get a raise everytime you do a good job. After all, this is expected from you and it is a prerequisite for you keeping your job for a long time. You can always ask for a raise, but that does not mean you will get one.
On the other hand as I mentioned earlier, either you changed the software's algorithm and implementation so much that you deserve a separate publication or you bug-fixed a crappy code (which you will use on your PHD) which does not really say that much. Either case, this is probably the only credit you will get.