I also use a Kobo with Calibre-web and it syncs fine. It’s been about a year so I can’t remember specifics. I remember modifying settings in my Kobo to point to my Calibre-web URL and in Calibre-web settings allow Kobo sync and then make a Kobo shelf. All the books in Kobo shelf are what it syncs too
Do you have conditional forwarding enabled in pihole settings? I think you need that.