The other answers provide decent general advice. But I fear that they lack the urgency that comes from having actually done this recently. For some background, I was just hired in the past 8 months as an assistant professor at a research university for a data science position, was also preparing applications for industry data science positions, and specialize in topological data analysis (TDA).
Say you want to be employable for data science positions (careful: "data analyst" tends to refer a different job) and get an industry job in a reasonable time frame at the end of a masters. You can do this in a theory-heavy course. If you are unfocused, it will cost you time (and salary) brushing up on skills during a job search after you graduate.
What masters courses should you look for?
It is absolutely essential that you find a course that helps you further develop a set of computer skills in addition to theoretical ones that will be visible to potential employers. An anecdote: I took an MSc like this, the courses included a full proof-based run through of Hatcher's algebraic topology. But also multiple courses on modern machine learning with significant coding components.
What won't help you get a job that quickly: Taking a course with no computational lectures, writing a very theoretical thesis without further developing your computational skills, and then throwing in your industry applications against computer science majors who won't cost an employer 6 months of time just to become productive. This isn't hypothetical: I've had multiple friends get done with very theoretical math PhD's, including specializing in algebraic topology, then take 6mo - 1 year of re-skilling and searching to get an industry job.
What skills are your target employers looking for?
I'd encourage you: Go look up job postings for data science positions you think you could be interested in, and look at the list of skills they'd like. They're going to include Python/R, SQL, probably familiarity with neural networks or CNN's, regrettably an increasing interest in Large Language Models, basic statistics, data cleaning, data visualization, etc. Some type of more serious memory management language like C++ couldn't hurt. Data science positions are also often interested in whether you have skills working with different types of data: Images, text/web scraping, "unstructured", geospatial.
You don't need to be an expert in all of them. Also, some demand for certain skills will change over time. You can't just blow building these up because they're all "easy", however.
What about more TDA?
If you take a Masters, TDA projects can be decent vehicles for a thesis that has some serious math while also benefiting from computer skills you want to build up to be competitive for industry position.
Computational topology and computational geometry for data analysis are not, however, particularly in-demand skills outside of academia. For example, persistent homology remains too expensive right now compared to much faster methods that are "good enough" for most use cases businesses currently care about. Obviously there's continual research work going into improving that situation, as the field is relatively young.
Which is to say, if you want to do more TDA/PH related work in a masters, but are angling for industry positions: It's something you can do, but you need to combine it with bulking up other skills.