Every browser context is its own storage partition. create_browser_context() hands you a browser_context_id; pass it to set_cookies(...) and get_cookies(...) and the cookie lives in that context alone. A cookie set on A never shows up when you read B, that wall is why one browser can hold many independent sessions.
context A 0 cookies
ctx_a = await create_browser_context() → 9F3A…E7
empty · no cookies
await get_cookies(browser_context_id=ctx_a)
isolated storage
context B 0 cookies
ctx_b = await create_browser_context() → 4B8D…C1
empty · no cookies
await get_cookies(browser_context_id=ctx_b)