You’d need to contact Spotify, they are responsible for what shows up in the Sonos controller under the Spotify area. As far as I am aware, they’ve been restricting podcasts from showing up there for quite a while. The cynic in me thinks they’d prefer to have you using thei app, rather than a ‘third party’ app. 

The cause (Spotify) is graphically illustrated (by me) here: Playing Spotify podcasts via Sonos | Sonos Community

Whenever anyone asks this question, they get the same reply (usually by the same people) explaining that the issue is with the third party provider. In this case it's Spotify, but they'll say the same thing for Google Podcasts.

Sometimes they'll say that Sonos makes the API available, so the third party should just use it. Unfortunately it's clearly not that easy.

Sonos needs to sincerely reconsider it's current podcast support and take an active role in cooperating with these third parties rather than wait for third parties to come to them like they're still the hot commodity. 

More people are choosing to control their podcasts with Google Assistant, and that means using either Google Podcasts or Spotify. It blows my mind that Google Assistant is natively integrated into newer Sonos devices, but you can't use Google Assistant to initiate podcast playback on the Sonos device. 

"It's their fault, they should come to us" is the swan song of a dying brand. I just hope Sonos doesn't fall irreversibly behind the voice controlled services trend. 

While I think I understand your perspective, what seems to be missing is the details of how Sonos works. Sonos has written an API that is open to all streamers who sign up for the program. The streaming company applies that API to their own servers, or stands up new ones that include that API and tell Sonos where to point the Sonos system to access that data. Sonos has no control over what the streaming company chooses to stream from that server, Sonos just points their client, running on the Sonos speakers, to the server owned and maintained by the streaming company. 

Voice control is a relatively new feature, and one that’s still evolving. It’s even more complex, due to the fact that you now have three companies involved, Sonos, the streamer, and the voice command company.

I certainly agree that there is work to be done on better integration, but it’s hard for me to lay all of this on Sonos. 

I do agree that a more (visibly) active involvement by Sonos in these things would help to build trust in the brand.

Sonos already has fantastic podcast support in their mobile apps, see here: https://developer.sonos.com/build/content-service-add-features/add-podcasts/

The issue is that music services need to do work to integrate their content, and Spotify can’t even be bothered to allow podcast search, never mind all the other features listed on the above page.

I recently discovered that BBC Sounds actually implements a lot of this for their podcasts. None of the other services I use seem to have done this work.