The styleOverrides feature of the theme is extremely powerful and versatile. In the Overrides based on props portion of the documentation, you can find an example of specifying a callback within the styleOverrides which then gives you access to the component's props and state (via ownerState) and the theme.

Below is an example showing how the callback syntax gives you access to the theme as well as showing how you can leverage ownerState to do conditional styles based on the props passed to a component (e.g. based on whether or not startIcon was specified or which variant was used or any combination of interest).

import * as React from "react";
import Stack from "@mui/material/Stack";
import Button from "@mui/material/Button";
import { createTheme, ThemeProvider } from "@mui/material/styles";
import SaveIcon from "@mui/icons-material/Save";

const theme = createTheme({
  themeName: "Default (Mortgage Hub)",
  spacing: 4,
  components: {
    MuiButton: {
      styleOverrides: {
        root: ({ ownerState, theme }) => {
          const conditionalStyles = {};
          if (ownerState.startIcon !== undefined) {
            conditionalStyles.paddingLeft = theme.spacing(6);
            if (ownerState.variant === "outlined") {
              conditionalStyles.border = "5px solid black";
              conditionalStyles["&:hover"] = { border: "5px solid grey" };
            }
          } else {
            conditionalStyles.paddingLeft = theme.spacing(4);
          }
          return {
            ...conditionalStyles,
            paddingRight: theme.spacing(4)
          };
        }
      }
    }
  }
});
export default function BasicButtons() {
  return (
    <ThemeProvider theme={theme}>
      <Stack spacing={2} direction="row">
        <Button variant="text">Text</Button>
        <Button variant="contained">Contained</Button>
        <Button variant="outlined">Outlined</Button>
        <Button startIcon={<SaveIcon />} variant="contained">
          Contained with startIcon
        </Button>
        <Button startIcon={<SaveIcon />} variant="outlined">
          Outlined with startIcon
        </Button>
      </Stack>
    </ThemeProvider>
  );
}