What is this strange pulse in my audio output?
Not really an answer but some hints on how to proceed.

You need to debug this on step at a time. Start with shortening the inputs to the Focusrite and disconnect the Linux computer entirely. If you still see noise, disconnect the power supply from you laptop and run battery only. If it's still noisy, either the Focusrite or the USB interface are bad (i.e. ground  provided by your USB port is just too dirty).
Then connect the Linux PC ground only (leave the inputs shorted).
Then connect signal as well but make sure the output of the Linux PC is all the way down and verify by measuring: should be zero volts.
Then play a -20dBdFS sine wave at 1kHz from the Linux PC. Compare that to expected results.

The fix will depend on where in the chain things go wrong. Audio connections are tricky and susceptible to power supply contamination, ground loops, Electro Magnetic Interference, etc.
Hence you should used balanced connections whenever possible. Try using the XLR inputs on the Focusrite by either using a properly configured &quot;mono to balanced&quot; adaptor cable. Means that you should NOT connect signal ground. You can play around with connecting chassis ground or not. The easiest solution would probably be to use a passive audio isolation transformer with a ground lift switch.  Something like this perhaps: https://www.audiopile.net/FDB-202 (I'm not affiliated).
Good reads about this: https://www.ranecommercial.com/kb_article.php?article=2107