I originally posted this on r/learnprogramming but received only one response. I think this may be a better place to ask this because this is specifically an algorithm question rather than a programming question

Context: As a Covid-19 summer side project, I'm working on an app that first prompts users to take a personality test. When they are done, they receive multiple scores corresponding to different personality traits. The purpose is to meet new friends who have similar personality scores as you. To generate user engagement, users have to press a button to be added to a list of people waiting to get matched (so that there is a level of intentionality when finding a match to avoid inactive users). From the moment the button is pressed, they should receive a match within 24 hours

In general, what is the best algorithm for this type of live matchmaking? From my preliminary research, this seems to fall into a class of problems called the "stable roommates problem". However, I'm struggling to find resources for a variation of the problem where: 1) New participants are frequently being added to the set of participants waiting to be matched 2) From the time when new participants are added to the set, there is a maximum time that they wait to be matched. This means that at any given moment, every user has a unique amount of time left to find their match

Given those two constraints, what is the optimal way for me to match users based on similar personality scores?