My recent personal experience booking the Swan, just for context if anyone is searching for answers or guidance in the future:
The Capital One Travel portal offered the lowest rate on a single room with 2 Queen beds with no view. Fiance used her CapOne card because it's a travel card so she got more miles booking thru the portal than had we used any other card. She received an email from CapitalOne almost immediately with 2 confirmation numbers, one of which was a CapitalOne confirmation number and the 2nd number was just listed as "Hotel Confirmation". I still have no idea what this second number is for.
Every 24 hour period after we booked the stay, I called the Swan and Dolphin number, (407) 934 - 3000, and went through the automated menu until I could speak to a representative. Since I made the booking shortly before 3 non-business days in a row, each representative told me it wasn't in the system yet. After the 2nd business day, the rep told me that they found it in their 3rd party booking portal, but the confirmation number was not yet available. The next day I called back and they were able to provide me with another 8 digit reservation number that I added to my Disney account and successfully link. For the record, this number does not match the same confirmation number that Disney now shows in My Plans. I basically have 4 different numbers between Capital One, Marriott/Swan, and Disney.
I learned that only the lead guest on the Marriott/Swan reservation can add that 8 digit number to their Marriott/Bonvoy account/app and the names have to match on both. I initially tried adding the reservation to my account rather than my fiance's, but got a technical error and Customer Service told me that only the lead guest can add it to their Marriott/Bonvoy account. This is important because the app provides a mobile key to enter our Swan room, provides for check-in/out information, as well as some other things.
The only thing I have not done is added myself to the reservation. I was told by a few parties I'd have to go through CapitalOne to get them to add me to the reservation. At this point, I don't think I necessarily need to because the reservation already accounts for 2 people, Disney allowed me to match myself to the 2nd guest, and I'm also a little worried it'll change the confirmation number(s) in some way.
This was definitely a process, and we won't be staying at the Swan until this Summer, but hopefully this helps anyone else looking to book in the future. (Also, you'll notice I spelled Capital One differently above, this is because I was purposely trying to make this post more easily searchable).