Aperture 3.6 with MacOS Mojave, version 10.14.2 - some photos lost.

Can't find "Rejected" and the "Trash album", as much I know my Aperture trash is empty at the moment,

Your screenshot looks, like the Recent and Trash have been hidden. Try the following:

• Hover the mouse pointer to the far right of the site "Recent". There is a hidden Show/Hide button.
• If this shows "Show", click "Show" to show your Trash and Rejected again. Then you can check, if there are any items to recover.

For example, in my Test Library:

Is your Aperture Library in your Pictures folder or another folder in your Home folder?

Some users needed to repair the permissions and file ownerships of their home folder after the Mojave upgrade.

If you have not done so, repair your home folder as described here:

Resolve issues caused by changing the permissions of items in your home folder - Apple Support

Perhaps this will allow Aperture to repair the library properly.

if your library is in the Documents folder instead of the Pictures folder - are you by any chance syncing the Desktop and Documents folder with iCloud Drive? That could damage your Aperture Library beyond repair, if it is in a synced folder.

Some cleaning applications to remove duplicates can also damage Aperture libraries, so that there is no way to repair them.

In that case use your backup to restore the library, but keep a copy of your current library, so you can recover any new photos from the current library.

Navigate to your Aperture Library, press and hold the Control key on your keyboard whilst clicking on the Aperture Library, you should get a drop down menu where you can select Show Package Contents, from there you should see the Masters folder. Click on that and you will be presented with a labyrinth of folders where you will find your images.

Before you restore from the backup, try to repair the library manually. Aperture tried it already, but Aperture has four different first aid option. If you have not done that already, try them all in turn.

To open the First Aid tools hold down the key combination ⌥ ⌘ while double clicking the Aperture library. Keep holding down the keys firmly until you are seeing the First Aid panel. Select first "Repair Permissions" from the panel. Then try the other options.

There used to be a fourth option "Rebuild thumbnails", but I do not see it any longer as well. Rebuilding the thumbnails can now be done from the "Photos" menu.

The albums in your "Recent" section are hidden. Have you checked the Rejected and the Trash album for photos?

And when you checked the Masters folder, how did you search it?

The folder Masters is organized by the date of the import session, not the date when the photos have been taken. You should be finding the missing photos in the folder for the year > month > day when you imported them.

Is there a "Recovered items" project or album among your library items?

Sometimes you will find files that have been lost and found after a repair in a special project with "recovered" in its name. Is there such a project?