The thing about programming actual DSP chips (that have a C/C++ compiler), is that for the most part it’s very much like programming on a PC. Usually the system will be set up to run an audio processing function whenever a block of N samples is needed to output. What you do in that function is largely the same from platform to platform.
Setting up the system that surrounds that audio processing function is arguably more embedded programming than DSP, and probably not wildly interesting to you.
There are of course some differences between platforms, in memory management and optimization options. And of course, many DSPs are fixed-point math only (like Blackfin), but these days, as beginner, there is really no point in delving into that.
Really, the actual audio processing code will be largely the same, and it’s the similarities between what you’d do on these platforms - the concepts - not the fine detail differences, that you want to learn first in DSP.
If you really want to write DSP code and get it running on something other than a PC, I’d highly recommend getting the Daisy. It’s pretty fast, has a decent amount of RAM, is floating point and all the shit which is not actually processing audio is mostly done for you. Of course it’s not a specific DSP chip, but generic microcontrollers are used more and more for DSP these days.
Another option would be to get a teensy 4 and the audio board, or the Bela (but that’s a bit more expensive).
But, if you really want to learn DSP coding with minimum hassle… you’ve got a PC or mac in front of you. Download JUCE, take the example VST/AU plugin FX and start doing something with the audio