Connecting Flight Questions / Who-What is correct?

Costco Wholesale....the membership and Visa Card Combo.
The front left corner just displays "Citi"....the front right corner displays "VISA signature"
It is gray or silver.

Looks like the Costco card used to have baggage delay coverage when it was under the AmEx program, but Citi has been cutting the benefits ever since it bought the program in 2017. One of the benefits cut from the card was baggage delay coverage.

For example, they removed a bunch of benefits from all Citi cards, including the Costco card, in 2019:

  • Worldwide Car Rental Insurance
  • Trip Cancellation & Interruption Protection
  • Worldwide Travel Accident Insurance
  • Trip Delay Protection
  • Baggage Delay Protection
  • Lost Baggage Protection
  • Medical Evacuation
  • CitiĀ® Price Rewind
  • 90 Day Return Protection
  • Missed Event Ticket Protection
  • Roadside Assistance Dispatch Service
  • Travel & Emergency Assistance

https://yourmileagemayvary.com/2023/01/17/citi-cuts-more-benefits-from-costco-anywhere-visa/
Might be worth checking your Capital One card for its travel benefits. I have a primary card we use for day to day stuff but we use a different card for all travel booking and purchases because it has better travel benefits.