Note that you don't automatically teleport to your co-op partner's location, so open the map to see where they are and then use Diablo 4 fast travel to get to the same area. The PS4 version probably has cross-play with the PS3 version though, if anyone actually still plays it on the PS3. After the invite or request is accepted the other player will appear next to you on screen, and you can then return to the game world to meet up. Once they appear on your friend list, you can begin Diablo 4 co-op with them by selecting their name and then choosing Invite to Party or Request to Join Party.

Every site Im finding that lists the games that are cross-generational cross-play dont list Diablo 3 as one of them, however.

It wasnt possible PS3 <-> PS4, but that could have been due to the massive architectural differences and might not be an issue for the PS5 and PS4.

If you can't find the person you want to connect with, it's probably because you aren't friends yet, but by following the Add a Friend prompt at the bottom of the screen you can enter their email address or BattleTag and add them directly from the game without having to visit the website. Based on history, most likely no, but Im not an expert. Here you'll see a list of your friends, with consoles having a separate tab for friends on their network. To start online co-op in Diablo 4, you need to open the map screen and then move across to the Social tab.

Ps4 diablo 3 cross platform