Fix regressions: Local UI state is not persisted and flickering

[KovalevAndrey]

Description

Fixes https://github.com/bumble-tech/appyx/issues/671 https://github.com/bumble-tech/appyx/issues/672

In this change introduced a bug where I accidentally started saving the state of the transition Box along with children UI state which was wrong. This PR reverts it back and now I only save the state of children UI and not the wrapping Box with transitions.

I checked out the repo in the issue and the bug seems to have gone:

https://github.com/bumble-tech/appyx/assets/5773436/9b502934-6651-4206-889f-b738880ada8e

Checklist

• [x] I've updated CHANGELOG.md if required.
• [x] I've updated the documentation if required.

[zsoltk]

Let's also reference #672 that if I understand correctly this also fixes along with #671 (let's provide an updated video capture where appropriate).