The Notifications tab at the bottom of the screen is a feed of what has happened, a history you can scroll back through. It is not where you decide which alerts you get. That is Manage account, then Notifications.
The two get confused constantly, so it is worth being clear: the tab shows what arrived, the settings decide what arrives.
How it is grouped
By time, newest first: Today, Yesterday, This week, This month, then Previous months. That structure is doing work. Anything under Previous months has been waiting a while, so something there you meant to answer has been waiting for weeks.
What lands in it
Whatever you have turned on. Coaches see clients posting exercise updates, marking exercises complete, and sending messages. Clients see the same three things coming the other way. Turn a type off in your preferences and it stops appearing here too. The feed reflects your settings rather than everything that ever happened.
An empty feed tells you which side you are on: clients are told they will receive notifications from their coach based on their preferences, coaches the reverse.
You can answer without leaving
This part is easy to miss. An exercise update in the feed can be replied to directly, and you can like it or add a reaction. For a coach getting through a morning's worth of updates, that is the difference between acknowledging twelve clients and acknowledging three.
A reaction is not a substitute for coaching, but it is a genuine signal that somebody looked. Clients notice the difference between a workout that was seen and one that went unacknowledged.
Keeping it manageable
Mark things read as you deal with them, and use Mark all as read to clear a backlog you have already handled elsewhere. Show read notifications, under Filtering in your preferences, controls whether read items stay visible. Turn it off and the feed becomes a to-do list rather than an archive.
Load more brings in older items; the feed does not load your whole history at once.
If it will not load
You will see "Couldn't fetch notifications" rather than an empty list pretending nothing happened. Refresh, and check your connection. The feed needs the network. If the alerts themselves are not reaching your phone, "Staying connected with app notifications" covers that separately.