I play the game on ps4 and whenever someone tries to invite me I just don’t receive anything.
Almost most of the time I have a badge next to (social), which seems like it is telling me that I have an invitation or something? I keep checking requests section + chat and everything, but I find nothing there.
I am still able to join groups though like without any invite, and I can invite people and it works just fine.
It is so annoying because I never know if an Overwatch friend wants me to play with them unless they text me, otherwise I wouldn’t know. 
This may or may not be relevant, but I was also experiencing this (though, on the Microsoft Xbox platform). For me, it was due to having disabled notifications as a workaround for an earlier Overwatch 2 crash bug.
Once I re-enabled notifications, group invites sent to me began working again.
I do not have a Sony PlayStation, but I think you can find the comparable settings in Settings > Notifications > Pop-Up Notifications … ensure both Messages and Invitations are “checked” (enabled). You may also need to adjust your account’s privacy settings to allow Anyone or Friends Only (not No One).
I hope that helps!
I think my notifications are enabled but I am going to check again and see. Thank you!
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So i may have found a solution, but this is only for ps5 and possibly ps4 users. Whomever cannot see invites needs to go in to their privacy settings and look for “communication and multiplayer” located in “users and accounts”. Switch to anyone on both tabs. If already on turn off then on. Hope this helps, it helped me.