[Regression]: Failure to capture console-logs from a third party extension

[shairoth12]

Last Good Version

1.46.0

First Bad Version

1.47.0

Steps to reproduce

1. Clone my repo - git@github.com:shairoth12/repro-playwright-3p-context-regression.git
2. Run pip install -r requirements.txt && playwright install chromium
3. Add a breakpoint in Line 42 of in tests/test_extension_console_log.py.
4. Run the test_extension_console_log in debug mode.
5. When reaching the breakpoint:
   In the browser's dev-tools, go to the console and see that the log "Test console log from a third-party execution context" appears.
6. Continue the test run - playwright doesn't catch the aforementioned log and the test fails.

Expected behavior

I expect that playwright will capture the console log "Test console log from a third-party execution context", triggered by the example extension

Actual behavior

The log isn't captured, even though it appear in the dev-tools's console window.

Additional context

I'm not sure whether this regression issue belongs here, since it's a result of this microsoft/playwright commit.
I verified that the test passes with playwright-python 1.47.0 and a manually reverted version of the files changed in the commit above.

Environment

- Operating System: [Ubuntu 22.04]
- CPU: [amd64]
- Browser: [Chromium]
- Python Version: [3.10]
- Other info:

[shairoth12]

@yury-s Thank you for the fix!