Today I pushed forward with the CAD design. Every step makes it more obvious why every single part needs to be modeled with exact dimensions.
In the screenshot below you can spot the main issue: the back tire clashes with the frame. On top of that, the front gear has barely a millimeter of clearance from the frame – way too tight. Definitely need more tolerance there. Tomorrow I’ll continue with the wheels, the front fork, and the saddle. Stay tuned!

Prototype bike frame