[Feature request] Saving or bookmarking Teal app state

Feature request to allow app user to save the state of a teal app (different from the default), possibly including
- enabled/applied filters on the RHS
- selected settings from the LHS encoding panels for each modules?

Following is the original suggestion by an expert teal app user/developer

> Would it be possible for the NEST team to implement something that enables a user to save the "state" of a NEST app? As ADS culture champion I have had this idea suggested to me twice by two separate people within the space of a week. My idea is that I could do a lot of custom filtering using the RHS filters (perhaps removing outliers or selecting only some patients) to get the data to a state that I am happy with. Then I could click some "save state of the app" button, which downloads a file storing the state of the app at that moment. Then, when I run the app again, I could click another "regenerate state" button so that the app could be restored to the original configuration. I think this would be really important because it would make the apps more FAIR.

### Definition of Done
* User would be able to save and restore the state of a teal app
* This includes filters and encodings

### Tasks
* https://github.com/insightsengineering/teal/issues/898
* https://github.com/insightsengineering/teal/pull/1011
* https://github.com/insightsengineering/teal/issues/1186
* https://github.com/insightsengineering/teal/issues/1188
* https://github.com/insightsengineering/teal/issues/1187
* https://github.com/insightsengineering/teal/issues/1185
* https://github.com/insightsengineering/teal.widgets/issues/238
* https://github.com/insightsengineering/teal.widgets/issues/239
* https://github.com/insightsengineering/teal.transform/issues/210
* https://github.com/insightsengineering/teal.transform/issues/211