Below is a link to the 3 available Photography plans. As you can see, Lightroom Classic is paired with Photoshop and 20GB of Cloud space. With Photoshop and Lightroom Classic you don't actually need the cloud space but its available if you want to sync photos from a smart phone or just ignore it.
https://www.adobe.com/uk/creativecloud/photography/compare-plans.html
I just hope there's a plan that doesn't require me to buy Cloud space, since that's another subscription....
The Photography Plan 20GB does not require you to buy "another subscription". The one us$9.99 plan is all you need.
$9.99 PHOTOGRAPHY PLAN (USA)
It does not require you to even use any of the 20GB (provided 'free' in the Plan). But if you have an iPhone, iPad, etc- then you can use it! Photos synced between all devices!
"My way of working is to store the pictures on my external hard disk to avoid being 'to tangled up' into software providers."
And that is exactly how Lightroom-CLASSIC works! Your files remain 'local'.
All is exactly like your old Lightroom v6.! Nothing changes for you when you install Lightroom-Classic except you have all the new features (and Photoshop, and a Portfolio site, etc).
The only 'change' is that you need the Adobe Creative Cloud Desktop App to- download, install the Apps, and verify your subscription status.
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