BTW, it is always a hassle to have many third party libraries which are not a common part of the OS. You depend on them and if they messed up something, your whole project is useless.
This is the price to pay if you are using an open source operating system like Linux.
You can of course use ALSA directly, see here:
https://github.com/fredvs/alsa_sound/But if you want to decode audio files, there is no "native" solution, you will need third-party libraries, like libogg, libflac, libmpg123, etc.
No need for FFT lib, there is "native" pascal version. And for reading audio from specific source there should be a way to do that from ALSA directly, avoiding any third party libs. And then, above all another IDE...
Of course, if you are a FFT and Pascal guru, you can create your own FFT.
I think there is Pascal code for FFT in FPC package.
In uos, there are FFTs used for example to get the frequency spectrum or create an equalizer without using any external FFT library.
But, if I may, processing the FFT is not the easiest part of audio management.