Data Segmentation by engaged day

We are exploring to do visitor segmentation based on monthly engagement and bucket them based on number of engaged days .

A User is called engaged user if he has done any clicks (success event)  in a Day. We would like to create a user segment for user who’s engaged days is greater than X days in a given month

We tried multiple solution , however we couldn’t segment user based on engaged day as segment are based on session then visitor but nothing on Days.

Our unique user identifier is more than 20 char so we couldn’t  leverage ever serialization procedure . Methods of Event Serialization

Appreciate you help , knowledge article (KB) to crack the engaged day segment for visitor.