[docs] Fix broken links (mui#43144)

docs/.link-check-errors.txt

@@ -1,5 +1,2 @@
 Broken links found by `pnpm docs:link-check` that exist:
 
-- https://mui.com/material-ui/customization/theme-components/#creating-new-component-variants
-- https://mui.com/material-ui/customization/theme-components/#overrides-based-on-props
-- https://mui.com/material-ui/react-grid2/#whats-changed

docs/data/material/customization/creating-themed-components/creating-themed-components.md

@@ -22,7 +22,7 @@ This guide will walk you through how to build this statistics component, which a
 
 ### 1. Create the component slots
 
-Slots let you customize each individual element of the component by targeting its respective name in the [theme's styleOverrides](/material-ui/customization/theme-components/#theme-style-overrides) and [theme's variants](/material-ui/customization/theme-components/#creating-new-component-variants).
+Slots let you customize each individual element of the component by targeting its respective name in the [theme's styleOverrides](/material-ui/customization/theme-components/#theme-style-overrides) and [theme's variants](/material-ui/customization/theme-components/#variants).
 
 This statistics component is composed of three slots:
 

docs/data/material/migration/migration-grid-v2/migration-grid-v2.md

@@ -80,7 +80,7 @@ The Grid v2 is marked as stable in Material UI v6, so the `Unstable_` prefix is
 ```
 
 Alongside the stabilization, the API has been improved.
-You can see the changes and further details on how to migrate in the [Material UI v6 upgrade guide](/material-ui/migration/upgrade-to-v6/).
+You can see the changes and further details on how to migrate in the [Material UI v6 upgrade guide](/material-ui/migration/upgrade-to-v6/#grid2).
 
 Finally, the original Grid component is deprecated and will be removed in the future, so we highly encourage you to migrate to Grid v2.
 

docs/data/material/migration/migration-v4/v5-component-changes.md

@@ -744,7 +744,7 @@ The props `alignItems`, `alignContent`, and `justifyContent`—along with their
 
 These props are now considered part of MUI System, not the `Grid` component itself.
 
-If you still wish to add overrides for them, you can use the [callback as a value in `styleOverrides`](/material-ui/customization/theme-components/#overrides-based-on-props).
+If you still wish to add overrides for them, you can use the [callback as a value in `styleOverrides`](https://v5.mui.com/material-ui/customization/theme-components/#overrides-based-on-props).
 
 ```diff
  const theme = createTheme({
@@ -775,7 +775,7 @@ If you need negative margins on all sides, we recommend using the new Grid v2 in
 + import Grid from '@mui/material/Grid2';
 ```
 
-To learn more about the Grid v2, check out the [demos](/material-ui/react-grid2/#whats-changed) and the [Grid migration guide](/material-ui/migration/migration-grid-v2/).
+To learn more about the Grid v2, check out the [demos](/material-ui/react-grid2/) and the [Grid migration guide](/material-ui/migration/migration-grid-v2/).
 
 :::info
 Grid v2 was introduced in Material UI v5.9.1 and features negative margins on all sides by default.
@@ -1862,7 +1862,7 @@ The following classes and style overrides keys were removed:
 
 These props are now considered part of MUISystem rather than the `Typography` component itself.
 
-If you still wish to add overrides for them, you can use the [callback as a value in `styleOverrides`](/material-ui/customization/theme-components/#overrides-based-on-props).
+If you still wish to add overrides for them, you can use the [callback as a value in `styleOverrides`](https://v5.mui.com/material-ui/customization/theme-components/#overrides-based-on-props).
 
 For example:
 

docs/data/system/styled/styled.md

@@ -24,7 +24,7 @@ The utility can be used as a replacement for emotion's or styled-components' sty
 It aims to solve the same problem, but also provides the following benefits:
 
 1. It uses a default `theme` if no theme is available in React context.
-2. It supports the theme's [`styleOverrides`](/material-ui/customization/theme-components/#theme-style-overrides) and [`variants`](/material-ui/customization/theme-components/#creating-new-component-variants) to be applied, based on the `name` applied in the options (can be skipped).
+2. It supports the theme's [`styleOverrides`](/material-ui/customization/theme-components/#theme-style-overrides) and [`variants`](/material-ui/customization/theme-components/#variants) to be applied, based on the `name` applied in the options (can be skipped).
 3. It adds support for the [the `sx` prop](/system/getting-started/the-sx-prop/) (can be skipped).
 4. It adds by default the `shouldForwardProp` option (that can be overridden), taking into account: `ownerState`, `theme`, `sx`, and `as`.
 

docs/pages/blog/mui-core-v5.md

@@ -236,7 +236,7 @@ declare module '@mui/material/Button' {
 
 <p class="blog-description"><a href="https://codesandbox.io/p/sandbox/stupefied-mclaren-ho4zs?file=/src/App.tsx">CodeSandbox</a></p>
 
-**Second**, you can add [custom variants](/material-ui/customization/theme-components/#creating-new-component-variants) to the theme, overriding the CSS for specific component prop combinations.
+**Second**, you can add [custom variants](https://v5.mui.com/material-ui/customization/theme-components/#creating-new-component-variants) to the theme, overriding the CSS for specific component prop combinations.
 
 ```jsx
 import { createTheme, Button } from '@mui/material';