If you are on Android I think Antennapod (and maybe Podcast Addict) have a setting to enable higher listening speeds.

On ios I have only found Audible which offers 3.5 speed but is not a good podcast app, but there probably are other apps out there.

I once heard in a podcast episode that there is a technical reason for the 3x limit in most apps (and that the 3x is actually just 2.9 or sth. because of that) Above that there apparently happen gaps in the audio or something (with the current implementation). I have not found a source for that though.

Regarding „saving time“ listening to podcasts I have had more success by switching to shows with good shownotes and chapter marks and then skipping the parts I don’t really care about. Especially with news podcasts I sometimes retain more information from skimming the description than from listening to the actual episode.

For enhancing the feeling of fast-talking cleverness that comes with 3x speed, I found it beneficial to listen to some normal speed episodes in between (solo comedy podcasts were a good choice for me).