Hey there yyj_jay,
Thanks for using Apple Support Communities. We understand that you're not seeing Low Power Mode as an available option on your MacBook (Early 2016) after installing macOS Monterey. Is that correct?
That's great troubleshooting you've done so far. Let's have you try a couple other troubleshooting steps. One would be to start up in safe mode. After you're in safe mode, restart the Mac to see if the option is available.
Our other suggestion is to test this in a new user account. We'll also include steps to do this.
How to use safe mode on your Mac
Set up users, guests, and groups on Mac
If you're still having an issue, we recommend getting in touch with an Apple Support Advisor: Contact Apple Support
Kind regards.