[Quoth]

A Kobo with page turn buttons. Some Kobo can use a BT Keyboard (but it disconnects quickly).
There are some Android eInk that can use USB, or use BT. Most of those have no page turn buttons.
Nothing has a built in keyboard now.

With the Kobo and Calibre to manage books you don't need to use internal directories to sort. Calibre anyway uses a folder/directory for each author and a folder/directory for each title in that.

A Libra 2 is 7″ with 300 dpi (a DXG is only 150 dpi) and has PDF crop, so works better for PDFs. I have a DXG and a Libra 2, so can compare.

I also have an 8″ Kobo Sage. The Pen is an option, but unlike Kindle Scribe there is true handwriting & shape conversion in Advanced Notebooks. Ebooks best annotated with touch keyboard and text. A PDF can be directly written on and copied back to PC, unlike Kindle Scribe which needs the PDF send to Amazon, a KFX downloaded and finally annotations emailed.

Your Kindle or hers (even if it stops working) can be used for Amazon purchases in a way that lets them be read on the Kobo. There is also the Kobo store.

Calibre will convert the existing DXG files to epub for Kobo.

I also have a 10″ approx Kobo Elipsa. It's heavy and a bit large for ebooks. I recently gave away a 10″ approx reMarkable. It's very limited compared to the Elipsa and best for PDFs and drawing, also less than about 1/5th of the document storage.

I did replace the battery (really a cell) in the DXG, but it was hardly worth it as it's such an inferior ereader to any of the Kobos. I do have two 6″ kindles too, a Kindle Keyboard 3 (ancient) and a Paperwhite 3. I gave away an Oasis as it was pointless compared to even the original Libra I have.