How to add Tapo S505 switch to Apple Home with Matter?

I was able to add one Tapo switch successfully after first adding it to the Tapo app, but I have not been able to do the same with the second switch. I’ve tried deleting and resetting them several times.

The only way I was able to get both switches to appear in Apple Home was by creating a new Home, but I would like them to be added to my original Home where all of my other devices are set up.

For context:

• These switches support Matter, but not Apple Home directly.
• I already have multiple other devices (including 4 Tapo plugs) working fine with Apple Home.

Could you please let me know what might be causing this issue and how I can get these switches added to my existing Home?

[Re-Titled by Moderator]

Original Title: Tapo S505 Switch - Matter