Despite what some staff believe, registering an Oyster card on the TfL website does not magically enable a discount to be set on it.
To be able to add a discount, the "Registered" flag on the physical card has to be set. Since National Rail Ticket Offices stopped handling Oyster in late 2019/early 2020, this can only be done through the Staff screens on a London Underground POM (passenger operated machine aka TVM.) And presumably on a TOM (Ticket Office Machine) at those stations that still retain them in staff areas.
This entails entering a Photocard Number (where no Photocard is required, most stations enter the location code instead) and a password for if you need to phone the contact centre with a query.
Once those have been provided, you can then proceed to either add a discount or just save the details without adding a discount. (If you want a Priv NR Only discount set, for example, as that can only be done at selected Elizabeth Line stations, but they won't do so if the card isn't registered.)
Unfortunately, not many LU staff are aware that this partial registration (buying a Monthly or longer Travelcard Season on Oyster requires a full registration, including a Photocard and contact details) without setting a discount is possible. Having worked in an NR Ticket Office that sold Oyster products, it's always been an option and that hasn't changed even with LU closing all their Ticket Offices.