Generally, I would use an input rather than a searchbox for this functionality. The searchbox has a built in dropdown and will require the user to click the choice in the list and then unfocus the searchbox by clicking outside of it or hitting enter before the searchbox takes its value. This creates a strange UI.
An input element would allow the user to type in text and press enter to have the repeating group reflect its results. In either case, the input’s value must be confirmed (no longer has a blinking cursor) in order for its value to be read.
In your video, I can see that you click the choice in the searchbox’s dropdown, but the cursor remains blinking because the input is still focused.
I’ve tried an input and it still doesn’t filter the RG. I have another RG with another Searchbox and this functionality works.
Another question, above I show how I’m setting the RG’s list and then reloading the page as I’m using URL parameters for navigation, does this break the searching either via the input or searchbox.