`@next/playwright instant()` clears testing cookies for other origins

[teamleaderleo]

Link to the code that reproduces this issue

https://github.com/teamleaderleo/playground/tree/repro/next-playwright-origin-cookie/next-playwright-origin-cookie-repro

To Reproduce

1. Clone the reproduction and switch to the repro/next-playwright-origin-cookie branch.
2. Open next-playwright-origin-cookie-repro.
3. Run:

npm install
npx playwright install chromium
npm test

The reproduction creates a Playwright BrowserContext, adds a next-instant-navigation-testing cookie for app-b.example, and then calls instant() for app A using baseURL: 'https://app-a.example/'.

The assertion inside instant() fails because app B's cookie has already been removed:

AssertionError: app B cookie was removed by instant() for app A

actual:   undefined
expected: '[1,"app-b",null]'

Current vs. Expected behavior

Calling instant() for app A can remove a next-instant-navigation-testing cookie that applies to app B in the same Playwright BrowserContext.

I expect instant() to clean up testing cookies that apply to the application URL it is controlling, without removing cookies for other applications.

Provide environment information

Node.js: v22.23.1
@next/playwright: 16.3.1-canary.8
Playwright: 1.61.1

`next info` is not applicable to this reproduction due to isolating the `@next/playwright` package behavior.

Which area(s) are affected? (Select all that apply)

Cookies, Testing

Which stage(s) are affected? (Select all that apply)

next dev (local), next start (local)

Additional context

No response