[Regression]: middle / modifier click intermittently fails to open a new tab on Playwright 1.62.x

### Last Good Version

1.61.1

### First Bad Version

1.62.0

### Steps to reproduce

1. `git clone https://github.com/YuriiMotov/playwright-1.62-new-tab-mre.git`
2. `cd playwright-1.62-new-tab-mre`
3. `npm install`
4. `npx playwright --version` - expected `Version 1.62.1`
5. `npx playwright test --repeat-each=25 --workers=16` - see several tests fail with `Test timeout of 30000ms exceeded`
6. Downgrade to latest working version: `npm pkg set devDependencies.@playwright/test=1.61.1 && npm install`
7. `npx playwright --version` - expected `Version 1.61.1`
6. `npx playwright test --repeat-each=25 --workers=16` - see tests pass

### Expected behavior

I expect tests pass on 1.62.x as it was on 1.61.1 and previous versions.

### Actual behavior

Several tests fail with `Test timeout of 30000ms exceeded`

### Additional context

Only tests that attempt to open page in a new tab are affected.

`--workers=16` here is to imitate overloaded machine. In fact in our case it fails with `--workers=1` in CI.

See report generated by Claude Code: https://github.com/YuriiMotov/playwright-1.62-new-tab-mre/blob/master/README.md

### Environment

```shell
System:
OS: Linux 7.0 Ubuntu 24.04.4 LTS 24.04.4 LTS (Noble Numbat)
CPU: (14) x64 Intel(R) Core(TM) Ultra 5 125U
Memory: 28.49 GB / 46.52 GB
Container: Yes
Binaries:
Node: 22.23.0 - /run/user/1000/fnm_multishells/1402339_1785955498713/bin/node
npm: 10.9.8 - /run/user/1000/fnm_multishells/1402339_1785955498713/bin/npm
bun: 1.3.8 - /home/yurii/.bun/bin/bun
IDEs:
VSCode: 1.124.2 - /usr/bin/code
Languages:
Bash: 5.2.21 - /usr/bin/bash
npmPackages:
@playwright/test: 1.62.1 => 1.62.1
```