What you do and how much should be defined in your project details. So that should drive the testing deliverables. I normally define a set of browsers and versions I am targeting, plus devices I will test. If the client wants more they can add it for a fee. I have worked on many projects where the testing was more effort than the build.
This does not even include real world user testing.
I have used the content below in contracts before. It’s from Andy Clarke’s Killer Contract. Hopefully this helps.
Browser testing
Browser testing no longer means attempting to make a website look the same in browsers of different capabilities or on devices with different size screens. It does mean ensuring that a person’s experience of a design should be appropriate to the capabilities of a browser or device.
We test our work in current versions of major desktop browsers including those made by Apple (Safari), Google (Chrome), Microsoft (Edge), Mozilla Firefox and Opera. We won’t test in other older browsers unless we agreed separately. If you need an enhanced design for an older browser, we can provide a separate estimate for that.
Mobile browser testing
Testing using popular smaller screen devices is essential in ensuring that a person’s experience of a design is appropriate to the capabilities of the device they’re using. We test our designs in:
iOS : Safari and Google Chrome
Android : Google Chrome
We won’t test in Opera Mini/Mobile, specific Android devices, or other mobile browsers unless we agreed separately. If you need us to test using these, we can provide a separate estimate.