I've figured out some of the seeds for some of the plants that are used in the shop icons:
Garden Plant: ??? ???? (it is not 000 0000.)
Prairie Star: ??? ????
Forest Sprig: I would like to assume it is 022 2222, but it looks a bit different.
Curling Vine: I would like to assume that it is 033 3333, but it looks a bit different. Just like in the case of the Forest Sprig, it is a bit lighter than in the shop.
Cactus: 044 4444 (0 rare traits)
Cave Blossom: 055 5555 (1 rare trait)
Tiny Tree: 066 6666 (0 rare traits)
Ancient Fern: ??? ???? (077 7777 doesn't work for some reason. 099 9999 works, but it doesn't look like the icon.)
Lil' Mushroom: ??? ???? (It is not 088 8888, which has 2 rare traits)
Desert Beauty: ??? ???? (It is not 100 0000, 101 0000 or 100 0001, but 101 0000, which has 2 rare traits, looks the most similar. Those are the only ones that I have tried.)
Also, this is unrelated but I put in my birthday and I got a four star plant! It's really fun to just input random numbers and see what I get. I give thanks to the dev who made this game.