In the latest Messages for Android Beta, scheduled send is broken due to a date validation bug. It won’t let you schedule messages after today’s date number in any month. So, for instance, today’s date is 29 November, 2023; it won’t allow any messages to be scheduled in December unless they’re scheduled on the 29th, 30th, or 31st. Also, it won’t allow any messages to be scheduled in 2024, for what I assume are similar reasons.
Reverting to the latest stable version fixes it and allows messages to be scheduled for any future date.
It was a huge pain, but I was finally able to do it by leaving the beta, uninstalling updates, clearing cache, restarting phone, and then updating the app. I finally got the non-beta version, and scheduled messages works.