chore: allow launchServer with a sharedBrowser

[dgozman]

Also merges BrowserDispatcher and ConnectedBrowserDispatcher.
Also add a basic multiclient test.

References #35987.

[github-actions]

Test results for "tests 1"

4 failed
❌ [default] › run-tests.spec.ts:1305:5 › should provide page snapshot to copilot @vscode-extension
❌ [default-reuse] › run-tests.spec.ts:1305:5 › should provide page snapshot to copilot @vscode-extension
❌ [default-trace] › run-tests.spec.ts:1305:5 › should provide page snapshot to copilot @vscode-extension
❌ [webkit-library] › library/browsercontext-pages.spec.ts:82:3 › should click the button with offset with page scale @webkit-ubuntu-22.04-node18

6 flaky

⚠️ [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
⚠️ [webkit-library] › library/ignorehttpserrors.spec.ts:30:3 › should isolate contexts @webkit-ubuntu-22.04-node18
⚠️ [webkit-library] › library/screenshot.spec.ts:205:14 › element screenshot › element screenshot should work with a mobile viewport @webkit-ubuntu-22.04-node18
⚠️ [webkit-page] › page/elementhandle-bounding-box.spec.ts:22:3 › should work @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
⚠️ [playwright-test] › ui-mode-test-watch.spec.ts:145:5 › should watch all @windows-latest-node18-1

39215 passed, 804 skipped
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Merge workflow run.