Hmm can you tell me more what steps you took.
I just installed burpsuite on my machine and i am using the 12.9.0
in the proxy settings of burpsuite i have set a listener on 127.0.0.1:8065
before starting cypress i did
export HTTPS_PROXY=
http://127.0.0.1:8065
export HTTP_PROXY=
http://127.0.0.1:8065
and then i did npx cypress open.
From this point on all traffic went into burpsuite.
I cannot show you screenshots now because at work environment and dont want to share links from my work. But when i'm home i will make a small video/screenshots of my work