To @Violator @Marek Wendorf or @MattGartzke can you remove the fixed label from the ticket subject? It's confusing a lot of people as all the issues are not fixed, and Mojang is using this ticket to track more issues than just what was initially reported by that one person.
From having similar issues before this update – in the past PS4 offline coop worked differently if all, some, or none of the profiles were logged into PSN. (In my experience, if none were logged in, it loaded all character saves from P1's profile, and if at least one player was logged into PSN then it loaded from each player's profile.)
For those with "L3 button is unresponsive" issues, it might be helpful to include in your comments if any players, some, or all are logged into PSN or not. (Not just if they have accounts.)
And in the meantime, if none are logged in, try logging in just P1 or both P1 + P2 into their own PSN accounts and see if that helps the issue.
MCD-4751
And note it was the person that created this ticket that added the "[Fixed]" to the subject line, not Mojang. Which should have been left for Mojang to update – the actual ticket status is still open, and in some reddit threads they have said they are still working on some issues around this, see this comment from Mojang: https://www.reddit.com/r/MinecraftDungeons/comments/jy1uvw/character_avail_are_only_from_who_launches_the/gdczo9s/
To @Violator @Marek Wendorf or @MattGartzke can you remove the fixed label from the ticket subject? It's confusing a lot of people as all the issues are not fixed, and Mojang is using this ticket to track more issues than just what was initially reported by that one person.
From having similar issues before this update – in the past PS4 offline coop worked differently if all, some, or none of the profiles were logged into PSN. (In my experience, if none were logged in, it loaded all character saves from P1's profile, and if at least one player was logged into PSN then it loaded from each player's profile.)
For those with "L3 button is unresponsive" issues, it might be helpful to include in your comments if any players, some, or all are logged into PSN or not. (Not just if they have accounts.)
And in the meantime, if none are logged in, try logging in just P1 or both P1 + P2 into their own PSN accounts and see if that helps the issue.