[Bug]: Regression in webdriver BiDi (for Firefox) caused by `install playwright binding lazily`

[whimboo]

Version

main

Steps to reproduce

Check the daily results for WebDriver tests for Firefox:

• May 16th - 8:35pm: 2969 passed (56.7m)
• May 16th - 2:32am: 3008 passed (55.1m)

Expected behavior

To see expected tests to still pass.

Actual behavior

Tests are failing with:

Error: clock.runFor: TypeError: this.global[kPlaywrightBinding] is not a function Full val: {"columnNumber":29,"exception":{"type":"error"},"lineNumber":394,"stackTrace":{"callFrames":[{"columnNumber":29,"functionName":"_promiseAwareJsonValueNoThrow/<","lineNumber":394,"url":"about:blank"},{"columnNumber":27,"functionName":"AsyncFunctionThrow","lineNumber":803,"url":"self-hosted"},{"columnNumber":8,"functionName":"_promiseAwareJsonValueNoThrow","lineNumber":396,"url":"about:blank"},{"columnNumber":32,"functionName":"evaluate","lineNumber":334,"url":"about:blank"},{"columnNumber":43,"functionName":"","lineNumber":0,"url":"about:blank"},{"columnNumber":62,"functionName":"","lineNumber":0,"url":"about:blank"}]},"text":"TypeError: this.global[kPlaywrightBinding] is not a function"}

Additional context

CC @dgozman @yury-s it looks like that #35976 regressed it.

Environment

As used by GitHub Actions