Can I load a season ticket onto an Oyster Card for travel within London Zones

I live within the London Zones.

This month I bought a monthly season pass for the first time and was issued with a paper ticket .  I would prefer to use a Smart card/Oyster card if I can.

The guidance on your website is confusing on this issue and when I've asked your staff (twice now) but I haven't had a clear answer.  Can I load a season ticket onto an Oystercard?  I do not need to use the London Underground in my daily travel. The Smart card map on your website says that I should use Oyster PAYG or Contactless - I'm concerned that I may end up paying more than a season pass if I do this.

In addition, my season pass covers London Stations which means that I can go to London Bridge without additional cost, if I use Oyster PAYG, would this still apply?