[web] Roll Chrome to version 137 and Firefox to version 136.

[harryterkelsen]

This updates the Chrome version used for testing to 137. It also updates Firefox to version 136.

This also updates how we set up Chrome Devtools Protocol to avoid focus issues when the page running the test isn't focused.

Fixes #168686

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[flutter-dashboard]

It looks like this pull request may not have tests. Please make sure to add tests or get an explicit test exemption before merging.

If you are not sure if you need tests, consider this rule of thumb: the purpose of a test is to make sure someone doesn't accidentally revert the fix. Ask yourself, is there anything in your PR that you feel it is important we not accidentally revert back to how it was before your fix?

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[mdebbar]

[mdebbar]

Wow, so this was the issue? Nice job tracking it down!!

[matanlurey]

Doesn't seem to work? All of the Linux web_skwasm_tests are failing.