If you intend to use Lr on your mobile devices then you can't avoid the cloud as it is the only way that the edited, rated, flagged images can be synced to Lr Classic & your NAS. At that point you can either delete your images from the cloud / mobile devices* or keep the images on the cloud / mobile devices*. With latter you can continue edit, rate, flag images on your mobile devices and in Lightroom CC / Classic whereas with the former approach the images exist solely on your NAS and can't be accessed on you mobile devices or Lr CC.
* deleting images from cloud also deletes them from mobile devices and vice versa.
Edit: words in bold text transposed.
No none of this is even remotely possible using any version of Lightroom. The only way to do this currently is to use a physical external disk (external SSDs are tiny and fast) and store a Lightroom Classic catalog+images on it.
As others mentioned, that's not possible.
How about you get one of these 2-in-1 tablets/laptops and then you could have it with you all the time and work on your images at any time? You could buy one of these amazing Samsung's portable SSDs (I love them) and load all your images onto one of these?
Something to think about