Short answer: Tap the bell icon at the top right of Home. Notifications has three tabs. Today lists what is due today, Upcoming shows scheduled doses for the next 7 days, and Reminders collects refill alerts, health checks and insights. Tap Mark all to clear the new count.
The sparkle icon next to Mark all (What's New) opens the list of changes in your version of the app.
The inbox is a list inside the app, separate from the alerts on your lock screen. To get alerts on your lock screen, set up reminders and allow notifications; see setting up reminders. If alerts do not arrive, see reminders not firing.