I believe the state deadline to do that was by the Friday after losing the job, and buried in the fine text is a line mentioning that certain info has to be submitted at least a day prior to that Friday. I didn’t have required information for the bureaucracy at that time and I really didn’t expect the process to take so long or to be so absurd.

you need to talk to someone about this because I really doubt whatever you perceived / were told is accurate. Also employers have a vested interest in you NOT applying for unemployment as many states require them to pay a portion of it when firing/laying off.