[Bug]: Record at cursor inserts stale/previous action after editing test while recording (browser focus loss)

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### Version

@playwright/test: 1.62.1, Playwright Test for VS Code extension: 1.1.19, macOS

### Steps to reproduce

1. Enable Show browser in the Playwright Testing sidebar.
2. Run a test so the browser is left open at a useful page state.
3. Place the cursor inside the test where new steps should be inserted.
4. Click Record at cursor.
5. Perform a few actions in the browser — they are inserted correctly at the cursor.
6. Switch focus to the editor and manually edit the test (e.g. tidy a locator, add a comment, delete a generated line, move the cursor).
7. Switch back to the browser without stopping recording.
8. Perform one more click/action in the browser.

### Expected behavior

Only the new action is appended at the current cursor position.

### Actual behavior

The new action is recorded, and an extra stale action is also inserted — typically the last (or penultimate) action from earlier in the same recording session, or sometimes from a previous recording session.

### Additional context

### Workaround
Stop recording before editing the file. After editing, click Record at cursor again and continue. That avoids the stale action, but significantly slows the record → tidy → continue workflow.

### Notes
If I stay entirely in the browser and never edit mid-recording, generation behaves correctly.
The failure is specifically tied to leaving the browser / editing the file while recording remains active, then resuming clicks.
This feels like the recorder’s internal action buffer / document rewrite getting out of sync with the editor buffer (similar class of issue to editing-while-recording problems discussed in #17771).

### Environment

```shell
@playwright/test: 1.62.1
Playwright VS Code extension: 1.1.19
IDE: Cursor (VS Code-compatible)
OS: macOS Darwin 25.x
```

Start by reproducing the issue with Record at cursor: perform browser actions, edit the test in the editor, then resume recording. Trace the recorder and document-rewrite flow across the browser/editor focus transition, using the behavior described in #17771 as context. Done means resuming recording inserts only the new action at the current cursor position, with no stale action from the current or a previous session.

Written by the indexing model from the issue text.