I use a Kobo Clara HD. It has a Kobo store where you can buy books, or you can use the “experimental web browser”, point it to libgen or your libraries website, and download whatever book you want.
More often than not though I just hook it up to my Linux laptop and transfer books via usb.
I use a Kobo Libra H2O which has been quite good to me. For people that want to take it to the next level, there's the calibre-web project[1]. It's able to tie into calibre and push books to kobo devices through the built-in sync command.
I have the same ereader, and I can understand the want for wireless book loading from a convenience point of view.
But from the “I don’t want to depend on proprietary software and/or require a privacy breaching login account” point of view, a Kobo is just fine. If you so desire, it’s just a USB drive with an e-ink screen attached. Connect - drop files - eject - read files.
Aha, this brand is easy to get ahold of where I am!
Googling suggests the “beta” browser has been beta forever; does the software never update?
And does the beta browser support multiple tabs and copy+pasting urls? (FanFiction doesn’t do ePub, but there are several helper websites that provide it if you can copy paste the FanFiction URLs)
More often than not though I just hook it up to my Linux laptop and transfer books via usb.