I am sorry that the OP feels "desperate and sad." I agree with the comments suggesting that happiness in life is very different from achieving some specific career. I also think a lot has to do with mindset.

That said, there are zillions of jobs for mathematicians (far from data science and finance being the only options) and many of them involve working with beautiful mathematical concepts. Here are some examples, in no particular order:

 - Use math to identify cases of gerrymandering and help create maps that are fair. This involves graph theory, geometry, metric spaces, and more. It's very cool and super relevant.
 - Become a senior scientist or research mathematician at a tech company, like the sort that hired Jennifer Chayes, Laszlo Lovasz, Katalin Vesztergombi, etc. There is plenty of beautiful work to do in graph theory.
- Social network analysis is a lovely blend of mathematics and sociology. I saw a great talk by Strogatz on this topic once. I imagine companies like Meta might have teams of mathematicians studying social network graphs.
- Topological data analysis (TDA) is beautiful to a lot of people, and involves mathematical concepts such as graphs, metric spaces, Betti numbers, and a whole lot more. There are government and industry research groups based on TDA, and it's a growing area. Lots of jobs.
- Work for a government intelligence service. Plenty of connections to graph theory, number theory, etc. If you like your government and believe its mission is protecting people, then this kind of work can be immensely rewarding.
 - Work for a government contractor, like the IDA in the USA. I know people in jobs like that who spend most of their time thinking about elliptic curves, group laws, error correcting codes, etc.
- Be an actuary. If you like probability theory and probability models, there are really fun topics that come up in this setting.
- I push back against the idea that there is no beauty in data science. Many data mining algorithms involve beautiful mathematics, like principal component analysis (eigenvectors, change of basis), singular value decomposition and separating hyperplanes, graph clustering algorithms, etc. Many companies have realized that if they want to get their modeling right, it's beneficial to have a trained mathematician onboard rather than only people who know how to run commands and have no idea why the algorithm works. I know data scientists who spend their time tweaking these algorithms to work in new settings, which means they are constantly playing with these beautiful concepts. Additionally, there is tremendous satisfaction in feeling like you created something that has the ability to really help a large number of people in their lives, e.g., statistical models to inform government policy and help lift people out of poverty, match people to jobs they will enjoy, help people who use drugs to get out of a state of addiction, etc.
- I know a lot of people who think Fourier analysis is beautiful and there's a whole branch of data science (spectral theory, time series models) where you get to play with this every day. Same for working for companies like Sound Hound or Shazam, and probably many others that I haven't listed (Zoom? Skype? How do they denoise? Some beautiful math must be in the background.)
- I concur with comments who said secondary school teaching can be a very fulfilling job, and one full of opportunities to enjoy (and share) the beauty of math. That's especially true if you work with the IMO team, programs for gifted high school students, etc. Such students can even do cool research and there have been lots of MO questions about that topic.
- I believe certain types of engineering use fairly sophisticated tools from analysis. Sadly, I'm not an expert in this.
- Text analysis, e.g., using and developing algorithms for determining authorship, extracting summaries, etc. Imagine developing an algorithm that can use Twitter data to figure out when an emergency is happening and then dynamically allocate government resources to help.
- Mathematical art, both creating it and using math to connect people with art in new ways (e.g., Google Deep Dream)
- Using math to create improved epidemiological models, e.g., while working for a hospital system, government, etc.

Others have compiled better lists than this, e.g., [the AMS has a list][1] including the following and also a list of other lists.

- Climate study
- Animated films
- Astronomy and space exploration

I guess the message I want to impart to the OP is that there's a lot to be excited about and a lot to look forward to. Now that you're a trained mathematician, you can go in many directions. For almost any passion, there is a way to connect it to mathematics and to bring the beauty of math into that world. Go explore and play!


  [1]: https://www.ams.org/education/math-work