#9156: tab synchronized mod variable storage (3/3)

[twschiller]

What does this PR do?

• Closes #9156
• Stacked on https://github.com/pixiebrix/pixiebrix-extension/pull/9155
• Cleans up browser.storage.session on tab closure and mod deactivation
• Refactoring: splits up stateController

Remaining Work

• [x] Rebase vs. main

Demo

• See Playwright test

Future Work

• Playwright fixtures to assert browser.session.storage contents, to automatically check that the tab/deactivation listeners are working properly

For more information on our expectations for the PR process, see the code review principles doc

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[codecov[bot]]

Codecov Report

Attention: Patch coverage is 88.11881% with 12 lines in your changes missing coverage. Please review.

Project coverage is 74.81%. Comparing base (8318d74) to head (86d0070). Report is 312 commits behind head on main.

Files with missing lines	Patch %	Lines
...ipt/stateController/modVariablePolicyController.ts	80.00%	8 Missing :warning:
src/background/stateControllerListeners.ts	88.23%	2 Missing :warning:
src/background/background.ts	0.00%	1 Missing :warning:
src/store/deactivateUtils.ts	0.00%	1 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #9181 +/- ## ========================================== + Coverage 74.24% 74.81% +0.56% ========================================== Files 1332 1364 +32 Lines 40817 42036 +1219 Branches 7634 7850 +216 ========================================== + Hits 30306 31448 +1142 - Misses 10511 10588 +77 ```

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[github-actions[bot]]

Playwright test results

 132 passed
 2 flaky
 4 skipped

Details

 Open report ↗︎
 138 tests across 45 suites
 25 minutes, 57 seconds
 86d0070
 For more information on how to debug and view this report, see our readme

Flaky tests

chrome › tests/pageEditor/addStarterBrick.spec.ts › Add starter brick to mod msedge › tests/pageEditor/addStarterBrick.spec.ts › Add starter brick to mod

Skipped tests

chrome › tests/regressions/doNotCloseSidebarOnPageEditorSave.spec.ts › #8104: Do not automatically close the sidebar when saving in the Page Editor msedge › tests/regressions/doNotCloseSidebarOnPageEditorSave.spec.ts › #8104: Do not automatically close the sidebar when saving in the Page Editor chrome › tests/runtime/googleSheetsIntegration.spec.ts › can activate a google spreadsheet mod with config options msedge › tests/runtime/googleSheetsIntegration.spec.ts › can activate a google spreadsheet mod with config options