Blogging Prompts: Fix caching issue with today's prompt for the prompts dashboard card

[wargcm]

See: #18429

Description

Adds:

• Fetching to various places in order to fix the current day's prompt showing outdated info
• An observer on the prompts managed object changing to update the dashboard card UI

Testing

To test:

• Enable bloggingPrompts feature flag
• Login if necessary and select a personal public blog
• Navigate to the 'My Site' dashboard
• On the prompts dashboard card tap on 'Answer Prompt'
• Publish the post
• Wait for the 'Post published' notification on the dashboard
• Verify a network call is made to fetch the current day's prompt and that it shows as 'Answered'
• Tap on 'Posts'
• Delete the prompt post you published
• Navigate back to the dashboard
• Verify it shows the prompt as unanswered (Note: Sometimes the backend takes a little to update so this might not show if done too quickly. Navigating to another page and back should update the prompt again.)

Regression Notes

1. Potential unintended areas of impact
   N/A

2. What I did to test those areas of impact (or what existing automated tests I relied on)
   N/A

3. What automated tests I added (or what prevented me from doing so)
   N/A

PR submission checklist:

• I have completed the Regression Notes.
• I have considered adding unit tests for my changes.
• I have considered adding accessibility improvements for my changes.
• I have considered if this change warrants user-facing release notes and have added them to RELEASE-NOTES.txt if necessary.

[alpavanoglu]

I cannot build his branch.

[wpmobilebot]

You can test the changes in WordPress from this Pull Request by:

• Clicking here or scanning the QR code below to access App Center
• Then installing the build number pr18842-ebfc7c4 on your iPhone

If you need access to App Center, please ask a maintainer to add you.

[wpmobilebot]

You can test the changes in Jetpack from this Pull Request by:

• Clicking here or scanning the QR code below to access App Center
• Then installing the build number pr18842-ebfc7c4 on your iPhone

If you need access to App Center, please ask a maintainer to add you.

[alpavanoglu]

Test case succeeded ✅