Windows 10: Why are taskbar tray icons not showing even when I have them enabled?

I have it on left taskbar.

:)

 

Taskbar Tray icon not showing

Always a good idea to read Blog posts for the known issues.

• [NEW] After upgrading to Build 22610, the “Show hidden icons” flyout in the system tray may disappear completely for some Insiders, even though it shows as “on” under Settings > Personalization > Taskbar and “Other system tray icons”. We are investigating the issue. As a workaround if you need access to the icons that would show in the “Show hidden icons” flyout, you can go right-click on taskbar to open the Taskbar settings page, navigate to the “Other system tray icons” and individuals toggle specific apps to “On” until the issue is resolved.
  

Announcing Windows 11 Insider Preview Build 22610 | Windows Insider Blog

It would be fixed in the future.

 

Notification/System tray programs showing wrongs icons

I'm not great with languages but what I see is right to left of the Notification Area. Mine is left to right:



Some adjustments can be made to what is shown is accomplished by clicking the small up arrow to get the full list. Also right-clicking the Taskbar and choosing Taskbar settings then going to the Notification area can lead to enabling or disabling features on the bar.

Can't say about the clock but that suggests the whole screen may have been rotated or flipped.

 

How show the date in the system tray having the small icons enabled

You don't need to expand the width of the taskbar, nor do you need a 3rd party app to do what you want.

Right click at the taskbar > Taskbar Properties > right side, turn off "Use small Taskbar buttons".
That's it.



My system tray screenshot :