Hey @weedor,
what you described is not a bug, it is the way Wordpress will work in the future.
I think you will experience the same, if you activate the Twenty Twenty-Two theme, which is a block based theme that relies on FSE.
This is also the way Cwicly is kind of following.
Regarding the favicon issue, you are right.
It seems that they (WordPress) made it worse with the recent changes.
The current way this option is implemented is a bad one, I think you are forced to use the default image block and then you are able to select your favicon, but not sure about it.
I know it is convenient to just pick your favicon from the media library, but let me introduce another method, which is even better (but not as convenient as you might be used to).
Personally, this is my go-to method because I find it a more complete solution which I can control 100%.
Here you can generate your favicon with plenty of additional options, which you can choose e.g. project base to have all cases covered.
The generated code you can simply post inside the Cwicly options:
Hope this helps for the moment.