Quest rewards not showing up on Xbox One or xbox app

I'm experiencing a similar issue as its only showing me the quests from the Microsoft Rewards app in the Game Pass quests area on my profile page rather than showing the Game Pass quests. They probably just haven't released them yet since the ones from
December and the ones on the MS Rewards app are still technically on going.

Are they the Game Pass quests or the Quests in the Microsoft Rewards app for Xbox?

Have you completed the set up here https://account.microsoft.com/rewards/?

Rewards quests for a month dont start on the first of the month,they start on the first Tuesday of the month in most regions so tomorrow will be the start of the month for quests.

Weekly quests go from Tuesday to Tuesday in most regions as well.

The daily quest often isn't there the day before a new set of monthly quests is going to start for some reason,no idea why.

have you installed the Rewards app on your Xbox?

if you have, start the Rewards app and there should be a button under
Weekly Set to Show All Quests.

or from the Xbox Home Screen, press RB once to go to the
Game Pass tab and Quests should be there as well.

This is very common with Xbox Rewards. As long as you have completed the necessary achievements they will eventually show up as completed in the quest.