Ok. I just tested this on Xbox and am having no issues with joining 3v3 lobbies as the 3rd and we weren't having any issues adding a 3rd. I'm also not seeing other reports of this. Possibly, it's a PS issue, but it also could be something with your club/accounts. Are you all on the same club or are any of you joining as a free agent?
Try clearing your cache and rebuilding the database with the steps here.
Also, try deleting the personal saved data for NHL 26. To do that, please follow these steps. There is the risk of losing offline saves and changes to settings you've made. Those should download from the cloud though. Go to Settings/Storage/System storage/Saved Data. Locate NHL 26 and delete the saved data.