PDFs are hard to read on a 6" screen, but otherwise just about any non-Kindle reader can handle side-loaded EPUBs without forcing you to use an proprietary bookstore or app store on the device.
You might take a look at PocketBook/Tea readers. They do have a bookstore feature, but you don't have to use it or even register the device to an account. If you've got a large book collection, the library management software on the device recognizes keywords and series information you attach in Calibre.
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