BookReader.sqlite is largely used for some of the information related to Kobo Plus and library borrowing. I understand it gets used for other things, but, I don't know what they are. From my experience, it should be fairly small. I would only expect a large size like that if you are borrowing books from Kobo Plus. Removing it isn't a real problem. But, if the sync fails afterwards, using the account repair should fix it.
And as @DNSB added, with the timestamp and the existence of the two extra files, that database is almost definitely broken. The two extra files should only exist for a short time as changes are made to database. When they are committed they should disappear. Delete the three files and let the device recreate them.
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