Where is the USB stick formatter, and the USB Iso Writer in Budgie and Gnome? I have tried the search box in menu.
I cannot find it the repository either (except for a Multi ISO Writer).

    spaarks it's a part of Disks. if you right-click an ISO file in the file browser (Nautilus) and pick "Open with other application -> Disk Image Writer" it'll pop up. 😁
    in Disks itself you click the right-hand "..." titlebar button and pick Restore Disk Image.