I have an older iPad, and sadly it won't run any recent iOS, so Calibre companion won't install. What other options do I have?

If your iOS is still recent enough to be able to use iCloud, you can use that. You don't need to install anything. Start with opening your Calibre library stored on disk — all your books should be there. Then go to icloud [dot] com and drag & drop all your books there. If you got a folder already named iBooks, excellent, use that one. If not, just create a new folder, and then, from the Files app on your iPad, navigate to that folder. Things in the ePub format (and any other that iBooks can open) should be immediately visible and you can view them directly in iBooks.