fix(mcp): clear backendPromise in onClose to allow backend recreation#40019

mlugo-apx wants to merge 2 commits intomicrosoft:mainmicrosoft/playwright:mainfrom

mlugo-apx:fix/mcp-clear-backend-promise-on-closemlugo-apx/playwright:fix/mcp-clear-backend-promise-on-closeCopy head branch name to clipboard