mushroom, toadstool, fungus
蕈 centers on fungal growths: mushrooms, toadstools, and similar fungi.
蕈 combines the plant radical 艹 with 覃, which likely provides the sound. The character is used for mushrooms and fungi, but the exact historical development is uncertain.
The plant top 艹 sits over 覃, which looks like a spreading underground network. Picture mushrooms sprouting from that hidden fungal web.
For ジン, imagine a magical mushroom genie emerging from the fungus: genie -> ジン, and the mushroom grants wishes.