[material-ui][Alert] iconMapping should also support variant

[alexismo]

The problem in depth

I already submitted an issue on Material-UI about this: https://github.com/mui/material-ui/issues/46857

Your environment

`npx @mui/envinfo`

  System:
    OS: macOS 15.6.1
  Binaries:
    Node: 20.19.2 - ~/.nvm/versions/node/v20.19.2/bin/node
    npm: 10.8.2 - ~/.nvm/versions/node/v20.19.2/bin/npm
    pnpm: 8.15.7 - /opt/homebrew/bin/pnpm
  Browsers:
    Chrome: 140.0.7339.81
    Edge: 140.0.3485.54
    Safari: 18.6
  npmPackages:
    @emotion/react:  11.14.0 
    @emotion/styled:  11.14.1 
    @mui/core-downloads-tracker:  6.5.0 
    @mui/material:  6.5.0 
    @mui/private-theming:  7.3.1 
    @mui/styled-engine:  7.3.1 
    @mui/system:  7.3.1 
    @mui/types:  7.2.24 
    @mui/utils:  6.4.9 
    @mui/x-date-pickers:  7.29.4 
    @mui/x-date-pickers-pro:  7.29.4 
    @mui/x-internals:  7.29.0 
    @mui/x-license:  7.29.1 
    @types/react:  19.1.10 
    react: ^18.3.1 => 18.3.1 
    react-dom: ^18.3.1 => 18.3.1 
    typescript:  5.5.4

Search keywords: alert, icon, iconMapping, variant

Search keywords:

[github-actions[bot]]

You have created a support request under the "Priority Support" terms, which is a paid add-on to MUI X Premium ⏰. Please validate your support key using the link below:

https://tools-public.mui.com/prod/pages/validateSupport?repo=mui-x&issueId=19521

Do not share your support key in this issue!

Priority Support is only provided to verified customers. Once you have verified your support key, we will remove the support: unknown label and add the support: priority label to this issue. Only then the time for the SLA will start counting.