Does their gpodder sync thing work again yet? That's the main reason I tried it out before, but it was inactive when I checked. NextCloud requires your own server, right?
For AntennaPod, there are fast forward and rewind buttons. You can set a preprogrammed duration for each button. I have my fast forward button set to 30 seconds to skip commercials.
In addition, for AntennaPod, you can set a skip x seconds on podcast start, so if the podcast normally has 2 minutes of ads, jibber/jabber upfront, you can skip it. Also same for the backend of the podcast you can skip x seconds of the end of the podcast. This provides a way to skip ads, smalltalk, or jibber/jabber at the end of a podcast as well.
Given all that, which is great, be aware that AntennaPod doesn't automatically skip ads on its own. You must press the preprogrammed duration fast forward button manually.
I use AntennaPod but don't love it. It can be quite buggy. Podcast length is never correct for example and will reach the end before the podcast has finished.
I use AntennaPod and it's okay, I love the look but the UX takes some getting used to and I have no clue if it can sync with a desktop client, I guess with Syncthing there probably is a way for almost any app but I doubt that's what you mean!
I use podverse and love it. the other foss setup I have used is antennapod and kasts synced with the gpodder plugin for nextcloud, but kasts was kinda buggy so I switched to podverse