Cypress always listens to its users and with latest version 10.8.0, Cypress has added experimental feature to support running tests in Safari browser.
In order to run the tests in Safari browser ensure
Latest version 10.8.0 is installed
Add playwright-webkit as dev dependency in your package.json or execute the command npm install — save-dev playwright-webkit
Once the above steps are completed, now open the cypress.config.ts file and set the experimentalWebKitSupport flag to true
And we are set to run our tests in Safari webkit browser
If you open the cypress test runner, you can see the webkit option
Test Automation Stack 
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