chore: existingDispatcher() is based on connection

[dgozman]

References #35987.

[github-actions]

Test results for "tests 1"

6 flaky

⚠️ [chromium-library] › library/chromium/oopif.spec.ts:284:3 › should click @chromium-ubuntu-22.04-node20
⚠️ [firefox-library] › library/inspector/cli-codegen-1.spec.ts:986:7 › cli codegen › should not throw csp directive violation errors @firefox-ubuntu-22.04-node18
⚠️ [firefox-page] › page/page-wait-for-function.spec.ts:104:3 › should work with strict CSP policy @firefox-ubuntu-22.04-node18
⚠️ [webkit-library] › library/ignorehttpserrors.spec.ts:30:3 › should isolate contexts @webkit-ubuntu-22.04-node18
⚠️ [webkit-library] › library/trace-viewer.spec.ts:1309:1 › should pick locator in iframe @webkit-ubuntu-22.04-node18
⚠️ [webkit-page] › page/page-screenshot.spec.ts:345:5 › page screenshot › should work while navigating @webkit-ubuntu-22.04-node18

39233 passed, 804 skipped
✔️✔️✔️

Merge workflow run.