Knowing when and how much information to disclose to someone who (may be) trying to help you can be a difficult balance. You are right to be cagey about providing information, but it might be OK based on a number of factors - Level of trust in the person helping you, certainty about their identity, their possible motives, and the sensitivity of the information being disclosed. Indeed low grade information. (IP address might likely fall into this category - more about that later) might slightly lower the bar for the other factors. High grade information (financial info) would probably raise that bar.
So let’s look at your situation:
“I was on the phone with playstation game support … employee ”. Salient factors might be - Who you contacted - Major well known company? (for example Codemasters) or some small relatively unknown developer. Who contacted who? (I’m assuming you initiated the support request?). How you got the contact details… Phone number on the game packaging?, or phone number from the company’s website whose address you got from the game packaging (note the chain of trust there) is probably ok. Googling “Supa-mega-blaster support” and blindly dialling the phone number from the top hit is much more dubious.
As for disclosing a public IP address - Mostly that’s not too dangerous. In theory, your internet router will block unsolicited traffic. Of course routers can have security issues or be configured insecurely, and some software might rely on opening ports inbound to work. In practice there are automated bots continually scanning the internet for any weaknesses so exposed. In short the bad guys don’t need to ask you for your IP address, they will find the IP addresses of vulnerable equipment anyway (a little off topic - but best practice is to make sure that your router password is secure, and that 'remote administration' features of the router are disabled).
What might he need it for? He might me able to look at the logs on the companies servers to see error messages related to your connections. He might be able to check how congested the internet is between that server snd your connection.
So putting that together - if the contact was initiated by you, to the support contact of a well known, reputable developer, then disclosing your public IP address should not be an issue.
The other contributors to this thread have answered the query regarding the difference between internal (private) ip addresses and your public ip address.