Connecting second bluetooth device fails

[Nicolas Krzywinski]

System:
Ubuntu 22.04
bluez version 5.64

Devices:
2x Playstation 5 DualSense Controllers

Problem description:
Connecting either of the controllers individually works without a problem. But when trying to connect both of them, the second fails.

Following sequence is typical and shows that there is no problem with the controllers itself:
1) connect controller #1 > succeeds
2) connect controller #2 > fails
3) disconnect controller #1
4) connect controller #2 > succeeds
5) connect controller #1 > fails

SOMETIMES it works though and I didn't found out what was different.
Connecting both of the controllers immediately after boot+logon works most of the times!

When connecting a controller fails, there is _nothing_ in syslog.
Both controllers have been paired successfully and marked as trusted devices.
The failing connect attempt of the second controller first shows the system notification "connected", followed by a "disconnected" approximately 10-20 seconds later.