There are many types of noise that can be experienced, and they usually have separate potential sources, so it’s probably best to qualify the type of noise first.
Noise could be analog or digital, and could originate from the power supply (eg 60/50Hz hum, or ripple), the Raspberry Pi, the sound card, or even the software - I’ve found many of the LV2 plugins to be great little noise generators.
The original poster mentioned “static”. To me, that implies a high pitched noise, and he said “pitch changes in the noise as LED’s blink”. I’m quite familiar with that sound, which I can reliably evoke by changing pedalboards from the Mod UI. I’ve identified it as digital noise from the Raspberry Pi. The transistors within are changing state thousands or millions of times per second. That creates EMI which gets inductively coupled into the signal lines of the audio card. Also, the Wi-fi module is sending/receiving data to/from my computer and I believe that can induce noise as well.
Three things helped my noise problem:
Housed my system in an aluminum enclosure grounded to the input/output jacks. Shunting whatever EMI to ground is the best solution I’ve found so far.
Physically separated the sound card from the Raspberry Pi. Yup, not the sexiest or practical of solutions, but it made a modest difference. I also tried placing a grounded copper sheet between the two. That actually didn’t make a noticeable difference.
Disabled WiFi (and/or bluetooth):
If you do that, you’ll want to make certain that you’ll still be able to connect via a wired ethernet connection, and be able re-enable wireless communications by removing those configuration lines.
As a less drastic measure you could also try triple clicking “The Button” to toggle the wifi hotspot to see if that makes a difference.