I love that there is stuff out in the world that is quite rare, like the talking whale, golden egg, odd beetroot, giant turnip, dark heart, and others. More industries could use these mythical finds. The following are meant to be similarly rare.
Unsettling brick: Chance for these when smelting bricks (and still counts as a brick). Image of a screaming face charred into the side. Inspired by the Bélmez Faces.
Fulgurite: Chance to obtain while digging sand. Occurs in real life when lightning strikes sand.
Cordyceps-riddled ant: chance to obtain while raiding an anthill. Probably could be a rare food too.
A Stranger crystal: Just like the strange crystal, but stranger. Maybe it could even be good?
Odd sphere: Found while digging, or maybe while chipping boulders. Based on Klerksdorp spheres but also something else I think, this wasn't the name I remembered for them nor the location.
Ancient coin: found via digging or mining.
Petrified wood: found in your mom's bedroom, or while mining.
Two-headed snake: found when picking up adders.
Mummified bird: found when harvesting salt. Based on a phenomena around soda lakes such as Lake Natron.
Edit: Round 2---------------------------------
Giant Geode: Found while mining, a large placeable geode. Similar to giant turnip. Maybe it's a table instead of a chair? They're frequently visited while en route to the center of the Earth in very realistic movies.
Palace of Ice: Found while digging snow, or maybe related to seasons someday. A formation of Needle Ice that resembles a fancy palace, in an abstract way. I used to to collect chunks of needle ice and use them as models for buildings. Decays?
Golden Yarn: Chance to be made when spinning yarn. Somewhat based on this, but that was straw so whatever. Could also be Golden Thread, when spinning silk. So long as it's absurdly rare like the golden egg it shouldn't be a farmable issue. Maybe an EXP event too?
Higher order terms Clover: I had a dream the night after failing to get a four leaf clover about finding a bunch of five and six leafed ones (and a two leaf clover).
Royal Jelly: Pretty sure this has been suggested before, just stealing it for a potential rare find from hives.
Lobster Mushroom: Based on the parasitic lobster mushroom which grows on lots of different stuff, could be rarely found when foraging correct mushrooms. I think the forageables need more of these ultra rare curios overall. The one time I found one of these in real life, I kicked over a mushroom angrily and the underside was coated with it. Too old to eat unfortunately.
Star Jelly: Based on this phenomena due to fresh nostoc usually. If you abuse weed killer in a gravel driveway you can get a pretty chronic crop of the nasty wrinkled stuff growing.
Edit: Third Batch
Mighty Ammonite: Similar to the giant turnip, a gigantic ammonite fossil found very rarely while mining which can be used as a seat. There are some pretty huge examples of these irl.
Inchworm: More extremely rare foragables! An inchworm, extremely small. Unfortunately the map indicator will probably ruin it though.
Trilobite: Yet another thing for miners to find occasionally. It could also be a slightly more common spawn like a glorified petrified seashell, and works for the fossil collection as well. I actually kindof wish there were rare curio collections, but that's a whole different topic.
Seductive Carrot: Carrots could use an absurdly rare curio find.
Immense Pearl: Better time than ever for this one with the pearl diver credo, a rare find when getting a pearl. It should probably have negative LP gain, based on this. Still usable in pearl recipes though, but it should be incredibly rare enough that its novelty is a big part of the value.
Migratory Coconut: Given all the birds we have lately, this could spawn upon catching a bird. I'm sorry if you need a source.
[Player's Name]'s Foot: based on the Salish Sea human foot discoveries (oh cool they found more recently!), any player who drowns or has their corpse decay in water generates a custom foot curio which is depositing in the global water pool.
Edit: Fourth Group sans a good idea or two
Murderous Reek: Rarely found from picking up a murder tracking scent. Or from creating one?
Right here on my list was the good one. I remember adding it right above the following idea. Ripperoni.
Disgusting Visage: Rarely found on metal paving. We have lots of different items that spawn on different surfaces, but none on metal. A tarnish in the shape of a pareidolia-esque face could be one that spawns on metal paving.
Anomalocaris: Rarely found while fishing underground. An ancient organism, they thought for a long time from fossils that it was multiple different creatures. Underground H&H seems appropriate for some ancient monsters.
Another
Rat King: A rare dead animal spawn. When multiple rats' tails become intertwined. Also could occur with squirrels, or even deer when their antler's get interlocked. This sort of thing seems just dark enough to fit perfectly in H&H.