There are TWO versions of Lightroom.....the one that uses local storage, and is the updated version of the Lightroom 6 that you have, is called Lightroom Classic (now currently at version 8.3). The other version is the cloud-centric app which is now call Lightroom Desktop, and that one does indeed require you to upload all the files to the cloud.
There is a version of the Photography Plan which includes Lightroom Classic, Photoshop, the cloudy Lightroom, and 20GB of cloud storage. If you have inadvertently purchased the other version of the plan, which is cloudy Lightroom only and 1TB of cloud storage, I suggest you speak to Adobe Customer Care and have them switch your subscription plan to the one that includes Classic. Both plans are the same price.
It depends which plan you go for. Assuming you go with the Classic version, obviously all your image files are held locally, so there's no question of them "being held hostage" by Adobe. In fact, even if you end your subscription you will still be able to run Classic in what's termed "reduced functionality" mode....which basically means the Develop and Map modules are disabled, but everything thing else (import, add metadata, export, print, etc.) can still be done. So you could even carry on using the Quick Develop module in the Library module to do some basic editing.
If you go with the cloud version, obviously all your images are stored in the cloud and will not be accessible using the desktop app when the subscription ends. However, Adobe has provided a stand-alone app (called the Lightroom Downloader) which will allow you to download a copy of all the images, complete with edits in XMP form, and you will have 12 months following the end of the subscription to download your data.