docs(browser-run): clarify Browser Rendering permission name

[pucedoteth]

Summary

Summary

Clarifies the Browser Rendering API Token permission name in Browser Run documentation.

The Browser Run documentation uses the Browser Rendering - Edit permission name, which may be confusing because the product is now called Browser Run. This change adds a note explaining that the permission is still listed under the Browser Rendering name.

Fixes #32594.

Testing

Documentation-only change.

Screenshots (optional)

Documentation checklist

• Is there a changelog entry (guidelines)? If you don't add one for something awesome and new (however small) — how will our customers find out? Changelogs are automatically posted to RSS feeds, the Discord, and X.
• The change adheres to the documentation style guide.
• If a larger change - such as adding a new page- an issue has been opened in relation to any incorrect or out of date information that this PR fixes.
• Files which have changed name or location have been allocated redirects.

[cloudflare-docs-bot]

Review

💡 2 suggestions found in commit 34d5f63.

👉 Fix in your agent 👈

Fix the following review findings in PR #32598 (https://github.com/cloudflare/cloudflare-docs/pull/32598).

Before making changes, review each finding and present a brief summary table:
- For each finding, state whether you agree, disagree, or need clarification
- If you disagree (e.g. the fix requires disproportionate effort for minimal benefit,
  or the finding is factually incorrect), explain why
- If you need clarification before deciding, ask those questions
- Then share your plan for which issues to tackle and in what order

After triaging, follow this order:
1. Post a comment on this PR for any findings you are skipping, with the finding ID and your reasoning.
2. Then commit the fixes for the legitimate findings.

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---

## Style Guide Review

### Suggestions (2)

#### SG-0d1f3c19caae · LLM-filler phrases
- **File:** `src/content/partials/browser-run/cdp-api-token-permissions.mdx` line 5
- **Issue:** Line contains `Note that this permission is listed under the Browser Rendering name.`
- **Fix:** Remove the `Note that` filler and state the fact directly, e.g. `This permission is listed under the Browser Rendering name.`

#### SG-370082d317e8 · LLM-filler phrases
- **File:** `src/content/partials/browser-run/rest-api-token-permissions.mdx` line 7
- **Issue:** Line contains `Note that this permission is listed under the Browser Rendering name.`
- **Fix:** Remove `Note that` and state the fact directly: `This permission is listed under the Browser Rendering name.`

Code Review

This code review is in beta and may not always be helpful — use your judgment.

_{No code review issues found.}

Conventions

_{No convention issues found.}

Style Guide Review

Suggestions (2)

File	Issue
partials/browser-run/cdp-api-token-permissions.mdx line 5	LLM-filler phrases — Line contains Note that this permission is listed under the Browser Rendering name. Fix: Remove the Note that filler and state the fact directly, e.g. This permission is listed under the Browser Rendering name.
partials/browser-run/rest-api-token-permissions.mdx line 7	LLM-filler phrases — Line contains Note that this permission is listed under the Browser Rendering name. Fix: Remove Note that and state the fact directly: This permission is listed under the Browser Rendering name.

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[pucedoteth]

/rebase