fix(expect): update docs to point to GenericAssertions instead of expect library (#20688)

Closes #20432.

docs/src/test-advanced-js.md

@@ -599,9 +599,10 @@ export const test = base.extend<{}, { server: http.Server }>({
 
 ## Add custom matchers using expect.extend
 
-Playwright Test uses [`expect` library](https://jestjs.io/docs/expect) under the hood which has the functionality to extend it with [custom matchers](https://jestjs.io/docs/expect#expectextendmatchers).
+You can extend Playwright assertions by providing custom matchers. These matchers will be available on the `expect` object.
+
+In this example we add a custom `toBeWithinRange` function in the configuration file. Custom matcher should return a `message` callback and a `pass` flag indicating whether the assertion passed.
 
-In this example we add a custom `toBeWithinRange` function in the configuration file.
 ```js tab=js-js
 // playwright.config.js
 const { expect } = require('@playwright/test');
@@ -672,6 +673,10 @@ test('numeric ranges', () => {
 });
 ```
 
+:::note
+Do not confuse Playwright's `expect` with the [`expect` library](https://jestjs.io/docs/expect). The latter is not fully integrated with Playwright test runner, so make sure to use Playwright's own `expect`.
+:::
+
 For TypeScript, also add the following to your [`global.d.ts`](https://www.typescriptlang.org/docs/handbook/declaration-files/templates/global-d-ts.html). If it does not exist, you need to create it inside your repository. Make sure that your `global.d.ts` gets included inside your `tsconfig.json` via the `include` or `compilerOptions.typeRoots` option so that your IDE will pick it up.
 
 You don't need it for JavaScript.

docs/src/test-api/class-test.md

@@ -2,7 +2,7 @@
 * since: v1.10
 * langs: js
 
-Playwright Test provides a `test` function to declare tests and [`expect` function](https://jestjs.io/docs/expect) to write assertions.
+Playwright Test provides a `test` function to declare tests and `expect` function to write assertions.
 
 ```js tab=js-js
 const { test, expect } = require('@playwright/test');

docs/src/test-assertions-js.md

@@ -3,20 +3,20 @@ id: test-assertions
 title: "Assertions"
 ---
 
-Playwright Test uses [expect](https://jestjs.io/docs/expect) library for test assertions. This library provides a lot of matchers like `toEqual`, `toContain`, `toMatch`, `toMatchSnapshot` and many more:
+Playwright includes test assertions in the form of `expect` function. To make an assertion, call `expect(value)` and choose a matcher that reflects the expectation. There are many [generic matchers](./api/class-genericassertions.md) like `toEqual`, `toContain`, `toBeTruthy` that can be used to assert any conditions.
 
 ```js
 expect(success).toBeTruthy();
 ```
 
-Playwright also extends it with convenience async matchers that will wait until
+Playwright also includes web-specific [async matchers](./api/class-locatorassertions.md) that will wait until
 the expected condition is met. Consider the following example:
 
 ```js
 await expect(page.getByTestId('status')).toHaveText('Submitted');
 ```
 
-Playwright Test will be re-testing the element with the test id of `status` until the fetched element has the `"Submitted"` text. It will re-fetch the element and check it over and over, until the condition is met or until the timeout is reached. You can either pass this timeout or configure it once via the [`property: TestConfig.expect`] value in the test config.
+Playwright will be re-testing the element with the test id of `status` until the fetched element has the `"Submitted"` text. It will re-fetch the element and check it over and over, until the condition is met or until the timeout is reached. You can either pass this timeout or configure it once via the [`property: TestConfig.expect`] value in the test config.
 
 By default, the timeout for assertions is set to 5 seconds. Learn more about [various timeouts](./test-timeouts.md).
 

docs/src/writing-tests-js.md

@@ -115,12 +115,15 @@ learn more about them.
 
 ## Assertions
 
-Playwright Test uses the [expect](https://jestjs.io/docs/expect) library for
+Playwright includes [test assertions](./test-assertions.md) in the form of `expect` function. To make an assertion, call `expect(value)` and choose a matcher that reflects the expectation.
-[test assertions](./test-assertions.md) which provides matchers like
+
-`toEqual`, `toContain`, `toMatch`, `toBe` and many more. It also extends
+There are many generic matchers like `toEqual`, `toContain`, `toBeTruthy` that can be used to assert any conditions.
-this library with the convenience async matchers that will wait until the expected condition is met.
+
-Using these matchers allows making the tests non-flaky and resilient. For example, this code will wait until
+```js
-the page gets the title containing "Playwright":
+expect(success).toBeTruthy();
+```
+
+Playwright also includes async matchers that will wait until the expected condition is met. Using these matchers allows making the tests non-flaky and resilient. For example, this code will wait until the page gets the title containing "Playwright":
 
 ```js
 await expect(page).toHaveTitle(/Playwright/);

packages/playwright-test/types/test.d.ts

@@ -2317,8 +2317,7 @@ interface TestFunction<TestArgs> {
 }
 
 /**
- * Playwright Test provides a `test` function to declare tests and [`expect` function](https://jestjs.io/docs/expect)
+ * Playwright Test provides a `test` function to declare tests and `expect` function to write assertions.
- * to write assertions.
  *
  * ```js
  * import { test, expect } from '@playwright/test';