Separate from Highlight (which uses the mark html element, and is already supported in mui-tiptap) and instead is part of text-styling (style tag on a span): https://tiptap.dev/docs/editor/extensions/functionality/background-color. But should have similar implementation in mui-tiptap presumably.
This extension is part of the general https://tiptap.dev/docs/editor/extensions/functionality/text-style-kit