I will have a look at my Windows computer this evening (I guess I will first need to remove the spider webs and the dust on that machine ...)
There is one option that you could try before, please connect one of the nucleo boards you own, with those boards you can be sure that the reset pin is properly connected and that you do not have an issue because of some missing cable (you wrote that debugging worked with ST-Link's IDE, so the chances are pretty slim, but still perhaps worth a try.)
You can also make sure that the STLink firmware on your STLink/Nucleos/Discovery devices is latest/greatest, connect them to STM32CubeProgrammer and it will allow you to check/upgrade the firmware.
Can you please tell me which Nucleo/Discovery board you own, I can then do the setup with the same board.
Did you build latest Texane (STLink) or did you grab a prebuilt version from the internet?
If 2nd case, please provide the link so that I can use the same version.
Same with arm-none-eabi-gdb, which version do you use, there are some versions that work well, others are not that good. This will bite you later during debugging, so let's make this sure right now.
Michael