fix: sticky launch errors (#324)

This fixes an issue that there were sticky launch errors. When the
[following code
path](a15f0f301b/src/context.ts (L307-L339))
was throwing, the Error was stored in the Promise and not cleared
afterwards, this meant:

- If a browser was not there and the user tried to install it via
`browser_install` it was never working since the error was sticky.
- If other errors like CDP is not available yet etc. error appear a
re-connect would not work - the MCP server would require a restart.

Test plan: Since we don't have any `browser_install` tests I added a CDP
test for now to cover this bug.

src/context.ts

@@ -299,8 +299,12 @@ ${code.join('\n')}
   }
 
   private async _createBrowserContext(): Promise<{ browser?: playwright.Browser, browserContext: playwright.BrowserContext }> {
-    if (!this._createBrowserContextPromise)
+    if (!this._createBrowserContextPromise) {
       this._createBrowserContextPromise = this._innerCreateBrowserContext();
+      void this._createBrowserContextPromise.catch(() => {
+        this._createBrowserContextPromise = undefined;
+      });
+    }
     return this._createBrowserContextPromise;
   }