Studio Code: Show a clear notice when AI is disabled for the account

[nightnei]

Related issues

• Fixes STU-2143

How AI was used in this PR

AI assisted

Proposed Changes

Let's print clear messages when Studio Code AI is blocked.

Classic UI	Agentic UI

Testing Instructions

See testing instructions in 163787-ghe-Automattic/missioncontrol

[gcsecsey]

Thanks @nightnei, this PR looks good to me.

I tested both the classic and agentic UIs after blocking usage on my account, and it works as described.

Screen	Classic UI	Agentic UI
Settings
Chat

[wpmobilebot]

📊 Performance Test Results

Comparing 39f4fba vs trunk

app-size

Metric	trunk	39f4fba	Diff	Change
App Size (Mac)	1378.84 MB	1378.85 MB	+0.00 MB	⚪ 0.0%

site-editor

Metric	trunk	39f4fba	Diff	Change
load	748 ms	1075 ms	+327 ms	🔴 43.7%

site-startup

Metric	trunk	39f4fba	Diff	Change
siteCreation	6481 ms	6539 ms	+58 ms	🔴 0.9%
siteStartup	2387 ms	2383 ms	4 ms	⚪ 0.0%

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Results are median values from multiple test runs.

Legend: 🟢 Improvement (faster) | 🔴 Regression (slower) | ⚪ No change (<50ms diff)