Issue/13268 persist activity type filters in parent vm

[malinajirka]

Partially fixes #13268

Merge instructions:

1. Make sure Issue/13268 implement clear and apply actions #13483 is merged
2. Remove not ready for merge label
3. Merge this PR

This PR adds support for persisting checked items when the user sets a filter on Activity Type filter screen and opens it again from Activity log. The items are intentionally not persisted when the user leaves the Activity Log feature completely.

To test:

1. Open My Site
2. Open Activity Log
3. Click on "Activity Type" chip
4. Select some items
5. Click on "x" in the top left corner
6. Click on "Activity Type" chip again
7. Notice none of the items is checked
8. Select some items
9. Click on Apply
10. Click on "Activity Type" chip again
11. Notice previously selected items are checked
12. Click on apply
13. Leave the Activity Log
14. Open Activity Log
15. Click on "Activity Type" chip again
16. Notice none of the items is checked

Test anything else you can think of (configuration change), clear action, leaving the screen, etc..

PR submission checklist:

• I have considered adding unit tests where possible.
• 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.

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You can trigger optional UI/connected tests for these changes by visiting CircleCI here.

[peril-wordpress-mobile]

You can test the changes on this Pull Request by downloading the APK here.

[zwarm]

@malinajirka
All works as expected. The selection is persisted until you leave activityLog. 👍