AI Chat storage notice should dismiss only after the first prompt is sent

[petemill]

(or the close button is pressed)

Test plan

From a query

0. Fresh profile (or freshly upgraded to the storage flag being unflagged)
1. Open AI Chat panel (or full-page)
2. Observe the storage notice shows
3. Submit a query to Leo
4. Observe the storage notice disappears
5. Close and re-open Leo
6. Observe the storage notice is still not there

From the close button

0. Fresh profile (or freshly upgraded to the storage flag being unflagged)
1. Open AI Chat panel (or full-page)
2. Observe the storage notice shows
3. Hit the close button
4. Observe the storage notice disappears
5. Close and re-open Leo
6. Observe the storage notice is still not there

[hffvld]

Verified on Galaxy Z Fold 6 using version(s):

Device/OS: Galaxy Z Fold 6 / q6quew-user 14 UP1A.231005.007 release-keys
Brave build: 1.75.159
Chromium: 132.0.6834.83 (Official Build) beta (64-bit) 

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STEPS:

1. Follow the STR/TP from AI Chat storage notice should dismiss only after the first prompt is sent #42853 (comment)
2. Verify

ACTUAL RESULTS:

• Verified that the Conversation history storage notice is shown when launching Leo for the first time.
• Verified that the Conversation history storage notice is not automatically removed when closing Leo or relaunching Brave if no queries were sent to Leo previously.
• Verified that the Conversation history storage notice is removed and not shown anymore after the first query is sent to Leo.
• Verified that the Conversation history storage notice is removed and not shown anymore after tapping the x button on the storage notice.

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1	2	3

[srirambv]

Verification passed on

Brave	1.75.164 Chromium: 132.0.6834.83 (Official Build) beta (64-bit)
Revision	befbba8d7568f8713d6f942f9a7350c59b57f20a
OS	Windows 11 Version 24H2 (Build 26100.2894)

• Verified steps from issue description
• Verified storage notification is dismissed when a query is posted
• Verified relaunching browser with the query doesn't show the message again
• Verified on clean profile closing the storage notification and restarting browser doesn't show the message again
• Verified reset conversation history via brave://settings/leo-ai doesn't show the message again

42853.-.A.mp4	42853.-.B.mp4