fix: decouple listNotifications from useProfileSyncing

[mathieuartu]

Description

This PR moves the notifications logic from useProfileSyncing to the Notifications context.

Related issues

Fixes: https://consensyssoftware.atlassian.net/browse/IDENTITY-14

Manual testing steps

1. Enable notifications
2. Disable profile syncing
3. Verify that the notifications counter has been updated

Screenshots/Recordings

Before

After

Pre-merge author checklist

• I've followed MetaMask Contributor Docs and MetaMask Extension Coding Standards.
• I've completed the PR template to the best of my ability
• I’ve included tests if applicable
• I’ve documented my code using JSDoc format if applicable
• I’ve applied the right labels on the PR (see labeling guidelines). Not required for external contributors.

Pre-merge reviewer checklist

• I've manually tested the PR (e.g. pull and build branch, run the app, test code being changed).
• I confirm that this PR addresses all acceptance criteria described in the ticket it closes and includes the necessary testing evidence such as recordings and or screenshots.

[github-actions]

CLA Signature Action: All authors have signed the CLA. You may need to manually re-run the blocking PR check if it doesn't pass in a few minutes.

[metamaskbot]

Builds ready [14982e2]

• builds: chrome, firefox
• builds (flask): chrome, firefox
• builds (MMI): chrome
• builds (test): chrome, firefox
• builds (test-flask): chrome, firefox
• build viz: Build System
• mv3: Bundle Size Stats
• mv2: E2e Actions Stats
• storybook: Storybook
• typescript migration: Dashboard
• all artifacts
• bundle viz:

  • background: 0, 1, 2, 3, 4, 5, 6, 7
  • common: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
  • ui: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
  • content-script: 0
  • offscreen: 0

Page Load Metrics (1848 ± 90 ms)

Platform	Page	Metric	Min (ms)	Max (ms)	Average (ms)	StandardDeviation (ms)	MarginOfError (ms)
Chrome	Home	firstPaint	632	2130	1704	345	166
		domContentLoaded	1519	2388	1824	190	91
		load	1562	2407	1848	188	90
		domInteractive	26	124	60	32	15
		backgroundConnect	10	64	27	18	9
		firstReactRender	17	102	41	28	13
		getState	5	55	14	13	6
		initialActions	0	1	0	0	0
		loadScripts	1106	1823	1333	155	75
		setupStore	7	65	29	23	11
		uiStartup	1836	2638	2141	207	99

Bundle size diffs

• background: 0 Bytes (0.00%)
• ui: -208 Bytes (-0.00%)
• common: 0 Bytes (0.00%)