Mixxx can do all of those things, it’s a free alternative to Serato DJ and similar. It’s super straightforward to playback audio slowed to the exact BPM you need, loop it, and/or play it in a different key. Give it a try!
Let me know if you need any help.
Hmm, it looks like the first few messages there are doing initial setup. After that, it looks like it’s having trouble loading some of its libraries. Then it isn’t able to read your sound devices. I haven’t run Mixxx with nixos or pipewire, but maybe try the flatpak? Sorry it isn’t running out of the box for you.