I’ve updated the OS to Big Sur, but it brought no changes on the problem.
Upgrading OS seldom fixes existing problems in my experience. Especially on old old stuff like your Express which is at least 9 years old.
Please post screenshots of the Airport Express setup as you see I have done.. there are more details and we might find something that explains the problem.. otherwise sorry but not much progress. If the iPhone now is working then that pretty well eliminates the Express as faulty. There are a couple of things that might help though.
Set IP to static.. when you set it just by swapped the setting you need to put the DNS in manually.. strange!! I just use same IP as the router or a public DNS like 8.8.8.8

Another factor that helps is using IPv6 set to link local only.. Click on Internet Options and select it.

When using ethernet select OFF for wifi.

And of course Network must be set to bridge at all times.. whether using join a wifi or by ethernet.

This option is hidden when using join a wireless network as it is not needed.
Still no luck the issue is out of my pay grade!!