Cottage living finding plants, dig for gems etc

depends on where you are, ingame time of day and season (if you got seasons), I find there is quite a good amount of stuff arround the park of Willow Creek, also try fishing.

I've been looking around the new world and so far only found a frog log. Those plants and gems must be well hidden if they are there!

I think there aren't any in the new world which kinda sucks because I was hoping it would be the world with the most resources.

There are only a few resources and no gems. You have only one spot for frogs, but you can find them in ponds. For gems you could ask the snail for a gift. Sometimes you have luck. I always activate the vulcano challenge for gems. You can also ask the rabbits and birds for gifts. Sometimes you get flowers or plants.
It takes a while but then you can find enough mushrooms everywhere.

The more time you spend in a neighborhood, the more wild plants, digsites etc. spawn.

I found feathers outside my home practically as soon as I moved into a farm I made in HoB. I do have a dog that has the hunting trait though, and I have a pee bush outside. I don’t have the wild foxes enabled on the lot either. And, I remember playing my twin witches with a cat and dog, they also had a Bush, that the cat or dog would get feathers from ( I believe after fighting a bird ). In the farm in HoB I moved into it was kind of hard to tell if something was there because it was a little raised piece of snow, and it was at night. I also have a pond with swans in it too, but I doubt that would have any effect.

I've found only blueberry and mushrooms in the new world. You probably know that you need to spend a certain amount of time in the hood for crops to spawn on community ground. Same in other worlds, hang out a day or two in the hood to find stuff to harvest. That said, my impression is there are fewer plants in Henford-on-Bagley than in worlds like Willow Creek and Oasis Springs. Your sim might be better off by purchasing a few fruits/veggies at the stall, to plant.

PS: Maybe you can visit a neighbor and harvest a plant there. Neighbor might get upset, but probably not until you got some crops into your inventory.

There is a problem with the plants dropping to dirt and have to regrow except for some berries. I think it is a glitch since last pack. The chocoberries near the The ones near the Creature Keeper never gets berries now. Most thinks pop back to a dirt pile if they like the tomatoe plant a tree and another plant near town square that aren't from Cottage Living pack. I took all mods out to see if it made a difference, it didn't. Not my computer either cause it is a brand new Alien with 2 TB of storage and much more. Found perfect plants I saved are good to go but if your plants are ready to harvest and you don't, when you get back there are gone. Check your family inventory incase. As for collecting, a bunch seem to missing unless you stay in the area long enough for them to show up. Willow Creek Community garden is not harvestable or any I visited. Really disappointed cause I love the gardening and got rid of seasons so it wouldn't mess with my plants.