Right :

when you submit your login credentials like username and password then you are getting token from your server then you have to store your token in your local-storage or as cookie like token : Your_token

Then in your router in your App.js check if you are having token or not like

{
   !localStorage.getItem('token') ? <Redirect from='/' to='/login' /> : ''
}        

Here if you don't have your token then you are redirecting to login else redirecting to your following page.

You can use your token as header in api calls and then you can check if your token is valid or not from your back-end if not then return with error message.

If your token is expire then you can set your token : ' ' in localstorage .Then you can redirect to login page from that api response.

Main thing is token create token which automatically expire as per your requirement and use it with local-storage or cookie.

you need to give type="submit" to button of your form in order to submit form

  <Button fullWidth type="submit" variant="contained">
                Sign In
              </Button>

if it still not working, use state instead

here what I did with your code :

  const getEmail = localStorage.getItem("emailData")
  const getPassword = localStorage.getItem("passwordData")

  const [values, setValues] = useState({
    email: "",
    pass: "",
    showPass: false,
  });

  const handleSubmit=()=>{
      if(values.email ==="admin" && values.pass ==="admin"){
          localStorage.setItem("emailData","admin")
          localStorage.setItem("passwordData","admin")
      }
  }



const handlePassVisibilty = () => {
  setValues({
    ...values,
    showPass: !values.showPass,
  });
};


  
return (
  
  <div>
      {
      getEmail&&getPassword?<Home/>:
  
      
    <Container maxWidth="sm">
      <Grid
        container
        spacing={2}
        direction="column"
        justifyContent="center"
        style={{ minHeight: "100vh" }}
      >
        <Paper elelvation={2} sx={{ padding: 10 }}>
          <h2>Welcome to Employee Management System</h2>
          <form onSubmit={handleSubmit}>
            <Grid container direction="column" spacing={2}>
              <Grid item>
                <TextField
                  type="text"
                  fullWidth
                  label="Enter your Username"
                  placeholder="Username"
                  variant="outlined"
                  required
                  value={values.email}
                  onChange={(e)=>{
                    setValues(prevState=>({...prevState,email:e.target.value}))
                  }}
            
                />    
              </Grid>

              <Grid item>
                <TextField
                  type={values.showPass ? "text" : "password"}
                  fullWidth
                  label="Enter your Password"
                  placeholder="Password"
                  variant="outlined"
                  required
                  value={values.pass}
                  onChange={(e)=>{
                    setValues(prevState=>({...prevState,pass:e.target.value}))
                  }}
                  InputProps={{
                    endAdornment: (
                      <InputAdornment position="end">
                        <IconButton
                          onClick={handlePassVisibilty}
                          aria-label="toggle password"
                          edge="end"
                        >
                          {values.showPass ? (
                            <VisibilityOffIcon />
                          ) : (
                            <VisibilityIcon />
                          )}
                        </IconButton>
                      </InputAdornment>
                    ),
                  }}
                />
              </Grid>

              <Grid item>
                <Button type="submit" fullWidth variant="contained" >
                  Sign In
                </Button>
              </Grid>
            </Grid>
          </form>
        </Paper>
      </Grid>
    </Container>
}
  </div>

);