Windows Explorer cannot display raw files, so it displays the DNG's embedded jpg preview instead.
You can have the preview display your edits by selecting the image in Library, and go to Metadata > Update DNG Preview and Metadata. This command is also available when right clicking the thumbnail.
I don't know where your DNGs come from, but if they are created by the DNG converter, there are three options for Jpg preview – None, Medium and Full size. Medium is only 1024 pixels on the long side.
If you stop paying for Lightroom, the Develop and Map module will stop working, but you can still export.
If you change OS to Linux, I suppose you could keep a Windows computer with Lightroom installed.