Does it have anything to do with "layer visibility" setting on certain scale range?
Have you tried to open the attribute table and select a certain point then choose to "zoom to selected record" to see if you can see anything?
Well, the things you have attempted are different from what I suggested. It is difficult to find out why with the limited information we've been given here. Are you able to see the attribute table with all the records?
When you are on the Item page of the layer, do you get anything to display in the Data tab? Better yet, the suggestion from @anbinh would be ideal to try, as it sounds as if you did not try it, that is opening the attribute table, selecting a feature and zooming to the selection.
Would you be able to share part of the file to try it out?
So you can see the data points in Map Viewer Classic (MVC) but not in Map Viewer (MV)?
May I ask how did you create the feature layer? Was it from a shapefile, FGDB, or a CSV with coordinates or addresses, or other?
When you added the .csv file, did you add it to Content using + New item OR did you import it directly into any of the Map Viewers?
Also, can you share an extract of the CSV file so I can test it?
In addition, have you checked the advice on CSV, TXT and GPS files in ArcGIS Online?