Yup, your choke pushrod and choke thermostat have been brutalized, and your choke thermostat is sitting all cattywompus. Probably happened when someone put on that '71 (+70 California) Carter BBS carburetor in place of the original Holley 1920. Good swap, but neatness counts, and that choke sloppiness is going to interfere with ease and consistency of cold starts. Go get that № 1231 electric choke kit, install it and adjust it, and your starts will likely get easier and more consistent.
Can't see from these pics how whoever did the carb swap handled the different fuel inlet location (front on the BBS, side on the 1920). If their fuel line work matches their choke work…clean that up, too; do the
fuel line mod, which will help with ease and consistency of
hot starting.