I sure wish Adobe would offer older versions of Photoshop for those of us who would be casual users and cannot justify the expense of buying the latest and greatest version. Don't say try the CC! I want nothing to do with the Cloud! I have Elements 2020, but sometimes I could use more features for photo restoration.
Just for clarity - you can use CC locally working on your PC and saving everything to disk drives on your PC. There is no requirement to use the cloud storage at all. Many users, including me, do this.
Yes, you need the creative cloud app installed on your computer, as that is how the various applications are installed and updated. Photoshop is then installed on your computer. Everything is really done on your computer. You can save images to the cloud, but that isn't necessary.
I still think it would be worth while for Adobe to offer older versions of its software at reduced prices and with the understanding there is no support available. Not all want to pay the high prices Adobe asks.