I tend to go for story-telling podcasts, and within those I gravitate towards Twilight Zone-style weird anthologies. I don't know how under-appreciated they are, but I rarely see the genre represented in discussions much.

Right now I'm finding a lot of great stuff in:

• The Other Stories (all kinds of stuff, they have a different theme every month or so)
• The Wrong Station (similar, but less likely to stick to a theme for a while)
• Gray Matter (lots of modern adaptations of older horror/sci-fi, like Lovecraft)
• The Antiquarium of Sinister Happenings (higher ratio of dumb stuff, but still some gems)
• The Program (Black Mirror-esque)
• The Truth (various radio plays. Many aren't sci-fi, but still weird in some way. Kind of reminds me of the bits of Inside No. 9 I've seen.)--

My two favorites are:

Darknet Diaries - a podcast about hackers, cybercrime and hacktivism.

Well There's Your Problem - a truecrime podcast about social murder A podcast about engineering disasters, with slides!

Cautionary Tales by Tim Harford

Knowledge Fight. Two great dudes who break down the insanity of Info Wars

Underunderstood - Favorite one but on hiatus because they all had kids; side project of some journalists trying to help people

Hyperfixed - New problem solving one from Alex Goldman of Reply All

The Turning - Each season explores an organization that people don't commonly call a cult (but probably should)

Shell Game - Funny and frightening exploration with LLMs

Articles of Interest. It's nominally a fashion podcast, but they tie it into lots of other topics: history, culture, identity, religion...

I've always liked 99% invisible

Dungeons and Daddies (not a BDSM podcast), an actual pay D&D podcast about four dads and a Honda Odyssey accidentally thrown into the forgotten realms.

The players are the writers and director from the rocket jump YouTube channel, they also made a show called videogame highschool. The DM is Anthony Burch, creator of "Hey Ash, Whatcha Playing?" As well as the lead writer behind borderlands 2 (and basically the reason it's a good game).

Two ordinary cops. It's two ex coppers talking about their time as coppers in the Northern Territory of Australia.

I don't know if they are under appreciated, but:

My brother my brother and me

The Adventure Zone

Sawbones

Never Post!

https://www.neverpo.st/

a podcast for and about the internet, it's my favourite

I Don't Speak German

Film Reroll

From Rewatch With Love, if you like James Bond rewatch podcasts. Finished now so you could watch/listen to them all.

NADDPOD is my jam right now, it's four comedians playing D&D

Kill James Bond

Ologies with Alie Ward, for fun dives into specific topics!

I have no way of evaluating what is popular or under appreciated but I just started listening to Too Many Tabs (Pearlmania 500) and I'm very much enjoying it.

If you like or care about clean energy, I’m a fan of Volts with David Roberts

If you have any interest in biology/neuroscience, Robert Sapolsky's Father-Offspring Interviews is fantastic

Not under appreciated at all, but the XFM shows (the Ricky Gervais show) are fantastic. Only mention because I'm not sure how popular/well-known it is globally.

If its new to you, OP, give it a shot.