So in summary:
When you had all your data in the old version of OD stored on your local Mac (on-demand disabled) and you upgrade to the new experience OD the following seems to happen:
Your OD folder with all your data is moved to a new hidden library folder on your local Mac like:
/Users/<user>/Library/Group Containers/UBF8T346G9.OneDriveStandaloneSuite/OneDrive.noindex/OneDrive
A new OD is created as a "location" that links to the hidden library.
The default "on-demand" is set and all your data in this new location OD has the cloud icon.
Select your folders in OD and right click "keep on this machine" and the check-mark icon is set next to the cloud icon.
Actually I don't understand the logic when these 2 icons are visible for an object. Maybe someone has an explanation.
Now click the cloud icon and after a while the cloud icon disappears.
The data is not downloaded, you can do it when Wifi is off.
I assume that OneDrive checks if the data in the hidden library is up-to-date compared with the data in cloud using some time-stamps or whatever.
The very good question is why this isn't done automatically and the poor users have to figure all this out and do it themselves.
It helps to reboot and do just one OneDrive operation at one time and wait until it finishes before doing the next folder.
For me Spotlight is working when the data is locally available (no cloud icon)