Store photos both on a desktop and on iCloud

The message "(39 items on This Mac Only" means, that you are having 39 items, that are not compatible with iCloud and cannot be uploaded. All other items have been uploaded to iCloud as they should.

You may have imported a few files to your Photos Library, that have not been copied into your Photos Library and are stored outside the library, referenced by Photos. Referenced items will not upload to iCloud. And you may have items, that are in an incompatible format.

This document describes what the status bar means, and what to do about it: About the status bar in Photos for macOS - Apple Support

Create the two smart albums described there and check, if these albums are empty:

To find the 39 items "on this Mac only":

1. Choose File > New Smart Album.
2. Name the Smart Album "Referenced" and select Photo - is - referenced. Click OK.
3. Select "Referenced" in the left sidebar.
4. Press Command-A to select all the photos in the Smart Album, and then choose File > Consolidate.

To find other incompatible items:

1. Create a new Smart Album by choosing File > New Smart Album.
2. Name the Smart Album "Unable to Upload" and set the three pop-up menus to Photo - is - unable to upload to iCloud Photos.
3. Select "Unable to Upload" in the left sidebar.
4. Press Command-A to select all the photos in the Smart Album, and then choose File > Export > Export Unmodified Original For (#) Photos.
5. In the dialogs that follow, choose the file name format and location for the exported photos. Click Export, then click Export Originals.
6. After the photos export, make sure the photos are all still selected in the Smart Album. Then right-click or Control-click one of them, and choose Delete (#) Photos from the menu that appears.
7. Click Delete, then click OK.

Yes. I do. See the following: Set up and use iCloud Photos - Apple Support

Note that there is an Optimize option. If you turn that on (I haven't) and your Mac is low on storage space then space-saving versions will be kept on your Mac. If you don't turn it on (or you do and your Mac is not low on space), full size originals will be kept on both your Mac and on iCloud.