<StyledTextField
	fullWidth
	id="email"
	label="Email"
	size="medium"
	value={emailAddress}
	onChange={(e) => setEmailAddress(e.target.value)}
	error={emailError}
	InputLabelProps={{
	  shrink: emailAddress != null && emailAddress != "" ? true : false,
	}}
	helperText={emailError ? "Please enter a valid email" : "Required"}
 />

const [passwordHasValue, setPasswordHasValue] = React.useState(false);
// For re-usability, I made this a function that accepts a useState set function
// and returns a handler for each input to use, since you have at least two 
// TextFields to deal with.
const makeAnimationStartHandler = (stateSetter) => (e) => {
  const autofilled = !!e.target?.matches("*:-webkit-autofill");
  if (e.animationName === "mui-auto-fill") {
    stateSetter(autofilled);
  }
  if (e.animationName === "mui-auto-fill-cancel") {
    stateSetter(autofilled);
  }
};
...
<TextField
  type="password"
  id="password"
  inputProps={{
    onAnimationStart: makeAnimationStartHandler(setPasswordHasValue)
  }}
  InputLabelProps={{
    shrink: passwordHasValue
  }}
  label="Password"
  value={password}
  onChange={(e) => {
    setPassword(e.target.value);
    ...
  }}
/>

import {TextField} from "@mui/material";
import {useCallback, useState} from "react";
const AutoFillAwareTextField = ({onChange, inputProps, InputLabelProps, ...rest}) => {
    const [fieldHasValue, setFieldHasValue] = useState(false)
    const makeAnimationStartHandler = (stateSetter) => (e) => {
        const autofilled = !!e.target?.matches("*:-webkit-autofill");
        if (e.animationName === "mui-auto-fill") {
            stateSetter(autofilled);
        }
        if (e.animationName === "mui-auto-fill-cancel") {
            stateSetter(autofilled);
        }
    }
    const _onChange = useCallback((e) => {
        onChange(e.target.value);
        setFieldHasValue(e.target.value !== "")
    }, [onChange])
    return <TextField
        inputProps={{
            onAnimationStart: makeAnimationStartHandler(setFieldHasValue),
            ...inputProps
        }}
        InputLabelProps={{
            shrink: fieldHasValue,
            ...InputLabelProps
        }}
        onChange={_onChange}
        {...rest}
    />
}
export default AutoFillAwareTextField