Salesforce Calendar lives in its own tab, not inside screen flows. Here are your real options, side by side.

The Avonni Calendar in step 2 of a screen flow, captured in a Salesforce org. Fictional data.
One drag, three things happen. Here is the sequence, screen by screen.



No Apex, no deploy. The configuration happens in the component builder, inside Flow Builder.
Avonni Flow Screen Components, in production or in a sandbox. Start free opens both links.
Point it at an object with dates, map the start and end fields, pick agenda, calendar or timeline.
Add an Update Record interaction to the drag event. That is what turns dragging on and saves the new time. Then test with Previous and Next.
Agenda, calendar, and timeline views on the same records.
Create and move events by dragging, right in the flow.
Point the calendar at any object with dates, configured in the builder.
Pick a slot or an event and the dates land in your flow.
Schedule across technicians, rooms, or teams, each on its own lane.
Working hours, available days, and no bookings in the past.
Paths 2 and 3, side by side. A custom flow screen component is a Lightning Web Component you build and maintain yourself.
Use Salesforce Calendar in its own tab. It works, but scheduling happens away from the guided process.
A custom Lightning Web Component you write, test, and deploy. This is the native way to stay in the flow.
Installed from AppExchange, configured in the builder, live inside your flow. No code.
Avonni Flow Screen Components. Free sandbox, 10 free production licenses. Start free opens the install links for both.