Customize: Tallying of settings modified during save starts before processing completes

[westonruter]

In #32941 logic was introduced to fix a situation where someone modifies a setting while saving is undergoing, so that once the save is completed the dirty state is restored. The logic however failed to take into account the processing state which is used for settings which require server processing before a save can be initiated. Widgets, for example, currently must undergo a update-widget request to obtain the instance data for the setting. The result is that currently if you make a change to a widget's title and then click Save & Publish while the update-widget request is being made, after the subsequent customize-save request completes the modifiedWhileSaving object will have the setting ID for that widget inside of it, and the resulting saved state will be set to false even though wp.customize.dirtyValues() is in fact empty.

[westonruter]

In 40627:

Customize: Wait for processing state to clear before starting to captureSettingModifiedDuringSave.

See #32941.
Fixes #40729.