It looks like most AI is implemented in soylanguages like Python, but I’m more interested in high-performance aspects. Does that matter at this point?
It does, because you're putting the cart before the horse TBH. Soy languages like Python already can be high performance because, as mentioned, areas where performance is critical are written in a mixture of languages like C, C++ and Fortran. I don't recommend pooh-poohing Python. It's suitable for beginners, but it's also suitable for experts. You can get a lot done in Python.
I would also recommend R. The language itself is pretty janky but since you mentioned substantial prior programming experience I don't think that will corrupt you. One of the key advantages with R is that it has widespread acceptance in academic research and there are various things you can do in R readily where a Python equivalent is either not obvious or will require substantially more effort. For instance, there seems to be a lot more you can do easily with meta-analysis in R vs. in Python. Data visualization in R has, in my experience, also been much less painful than in Python. So-called "data wrangling", too, and I would recommend looking into the principles of "tidy data", which apply just as well in Python as in R, or just about anywhere else.
Since you mentioned "high-performance aspects", obviously that exists too, because something like pure Python isn't suitable for crunching huge amounts of linear algebra code. But it's best for didactic purposes to learn from the tools that already exist.
Here is an idea I may want to pursue: developing an AI that can write programs (perhaps games and DSP programs, but potentially other areas).
DSP will almost certainly be the easier of the two, depending on the scope. If you can marshal a dataset of inputs and expected outputs that you would expect a human programmer to figure out manually, then the task is straightforward. Like, if you start with input audio and you expect an output where background noise is suppressed, then that's something machine learning can do fairly easily in the scheme of things.
Games are another story entirely. Do you intend to write machine learning code that is a strong player in a game or the like? Single- or multi-player? It's pretty open-ended.
I’m experienced with system and embedded systems programming, and also DSP
That's good news because you have a) substantial programming experience, b) probably a decent amount of sys admin experience to get all of that to work and c) some mathematical background, which most likely includes a fair bit of probability and statistics if you're using DSP.
I don’t really do webshit aside from getting sockets to work.
I don't think that's going to be a huge problem, but it depends on what you want to do. FWIW, there's a decent amount of data science code out there that will automatically generate front-end webshit code based on your data and what you want to do with them.
Shiny is a good example.
Lastly, while the hardware recommendations for things like large language models mentioned in this thread are probably accurate, you can learn the fundamentals and still get a lot done with much more modest hardware.