Boarding passes

Do you have the app for the particular airline you have the pass for? I know with my passes, they generally automatically appeared when I was at the airport. It could be a location issue and they will only automatically appear when you are at the airport, or have location services turned on for that airline app. Also check Location Services for your Wallet.

Read this carefully, especially the last two sections.

Add and manage passes in Wallet on iPhone - Apple Support

I've not noticed that with the forum, but then I don't generally use an iPhone to access the ASC. Given that the forum can experience hiccups occasionally, it wouldn't be unusual, but I've always seen my local time when I post. I don't use Southwest, so I cannot really speak about their app, but I've not experienced any issues with United or American in the last couple of months with notifications appearing on the lock screen I just have to tap to get the boarding pass to appear. You could try removing the passes from the Wallet, and then force restart the phone, and add them back again. See what that does, because it appears the settings you describe sound correct.