Most data collection workflows will involve feature layers with editing enabled. Markup is a simple method intended to capture sketches and notes on a local device. The original data capture app ArcGIS Collector did not have Markup, but the free/cheap version Explorer did, and this came to Field Maps with the merger of all map-centric apps.
The markup is not associated with your map. It can be shared. Most practically it will be shared as an image, similar to adding notes to a pdf exported from Pro. You can share the raw markup data, but there are some limitations. You can open the markup on another Field Map or have a Creator publish it as a markup item and then add it to a map, access it in Pro etc. But again users would have to find and add it to the map.
So in your case, you can add the Markup to a Field Map and open it on top of the map. Or you can upload it to ArcGIS Online (Creator/Pro licence) and add it to the same map as a markup item in the Web Map or ArcGIS Pro.
https://doc.arcgis.com/en/field-maps/android/help/markup.htm
Long term, if you have users intending to make notes or capture data in the field, I would recommend setting up the device for that purpose - i.e. using a licence + Hosted Feature Layers. Mark-up is otherwise fine, but it will be a bit more limited for its purpose.
https://doc.arcgis.com/en/field-maps/android/help/design-an-editable-layer.htm
https://doc.arcgis.com/en/field-maps/android/help/capture.htm
