## The basics
- [x] I [validated my changes](https://developers.google.com/blockly/guides/contribute/core#making_and_verifying_a_change)
## The details
### Resolves
Fixes https://github.com/google/blockly-keyboard-experimentation/issues/563
### Proposed Changes
This expands the functionality introduced in #9213 to also include widget divs.
### Reason for Changes
MakeCode makes use of widget div in several field editors, so the issues described in https://github.com/google/blockly-keyboard-experimentation/issues/563 aren't fully mitigated with #9213 alone.
This PR essentially adds the same support for auto-closing as drop-down divs now have, and enables this functionality by default.
Note the drop-down div change: it was missed in #9123 that the API change for drop-down div's `show` function is actually API-breaking, so this updates that API to be properly backward compatible (and reverts one test change that makes use of it).
The `FocusManager` change actually corrects an implementation issue from #9123: not updating the tracked focus status before calling the callback can result in focus being inadvertently restored if the callback triggers returning focus due to a lost focus situation. This was wrong for drop-down divs, too, but it's harder to notice there because the dismissal of the drop-down div happens on a timer (which means there's sufficient time for `FocusManager`'s state to correct prior to attempting to return from the ephemeral focus state).
Demonstration of fixed behavior (since the inline number editor uses a widget div):
[Screen recording 2025-07-08 2.12.31 PM.webm](https://github.com/user-attachments/assets/7c3c7c3c-224c-48f4-b4af-bde86feecfa8)
### Test Coverage
New widget div tests have been added to verify the new parameter and auto-close functionality.
The `FocusManager` test was updated to account for the new, and correct, behavior around the internal tracked ephemeral focus state.
Note that some `tabindex` state has been clarified and cleaned up in the test index page and `FocusManager`. It's fine (and preferable) for ephemeral-used elements to always be focusable rather than making them dynamically so (which avoids state bleed across test runs which was happening one of the new tests).
https://github.com/google/blockly-keyboard-experimentation/pull/649 includes additional tests for validating widget behaviors.
### Documentation
No new documentation should be needed here--the API documentation changes should be sufficient.
One documentation update was made in `dropdowndiv.ts` that corrects the documentation parameter ordering.
### Additional Information
Nothing further to add.
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