Ability to 'time travel' during cypress run --headed

### Current behavior

When running Cypress tests in headed mode using the command cypress run --headed=true, the Time Travel Feature is not available for debugging. This issue is occurring from Cypress version 13.6.1.

### Desired behavior

The Time Travel Feature should be available for debugging when tests are run in headed mode, similar to how it functions when starting tests with cypress open. This feature works perfectly fine in the interactive mode and is a crucial tool for debugging tests.

### Test code to reproduce

1. Install Cypress version 13.6.1.
2. Create a sample Cypress test.
3. Run the test in headed mode using the command cypress run --headed=true.
4. Observe that the Time Travel Feature is not available for debugging purposes.

### Cypress Version

13.6.1

### Node version

latest

### Operating System

Windows

### Debug Logs

_No response_

### Other

_No response_

Reproduce the issue with Cypress 13.6.1 on Windows using cypress run --headed=true, then compare its behavior with cypress open. Trace the headed runner's handling of the Time Travel Feature and identify the relevant runner entry points or tests; done means time travel is available for debugging in headed runs without breaking interactive mode.

Written by the indexing model from the issue text.