Update:
Bambulab Support suggests basically I am just stupid and should look for small bending radius along the PTFE tubing. Just wow.
I saw on printables that some X1C users seem to have the same issue. I am currently printing a rising adapter to increase the height of the top glass of about 50mm (some prints only suggested 10-20mm). I tested this via simple blocks and a shady setup and with 50mm more height it seems to load and unload correctly.