The challenge with fungal-dominated environments is the absence of energy input. Fungi are decomposers, which means that they simply break down the hard work of other organisms, both flora and fauna. By their very nature, fungal ecosystems are ephemeral- that's why many mushrooms produce spores to survive and spread between the periods of food drought.
Additionally, the main part of any fungi is not the part above ground. It's a common misconception, but the largest portion of any fungus remains underground in the matrix of mycelium and hyphae. The part that breaks the surface is the sporocarp (aka a fruiting body), and has one goal- to spread spores as far as possible.
But neither of those points should be a true challenge to a worldbuilder! Let's talk about each of your biomes with those things in mind.
Forest-like
Check out the answer here. There are some challenges to fungal forests, but because the mycelium is always bigger than the fruiting body, the ground beneath a fungal forest is going to be almost entirely mycelium. This would give it a tough, solid texture due to the interwoven and tightly packed strands of hyphae. The ground structure would be very dense to support the large fruiting bodies without letting them fall over.
It'd be unlikely to find a producer in this environment. Thick, tightly packed ground that actively fights intrusion is unlikely to support much in the way of terrestrial plant life as we know it. As noted in the linked question, you'd probably have to get the energy from somewhere else in the world.
Fungal marshes
Fungi, while found pretty much everywhere, aren't overly fond of sitting water. Check out the link here for a small background in aquatic fungi. Essentially, fungi like to be near the edges of pools of water because there's no food in the middle. As far as soil type goes in a marsh-like environment, expect soggy, squishy masses. Fungi will gather around the edges of the pools and expand from there in both directions, breaking down material as they go. This would lead to a spongy, collapsible, quite unstable soil matrix that's probably still saturated with water and thus very squishy.
The perk of marshes is that they're already in a state of flux, which means we don't need a producer as desperately as forests would. Water is great for transporting nutrients and sugars, and if there's a slow flow of water through your marsh, whether from rainfall or tides or a slanted water table, the fungi will be quite happy.
Fungal plains
This is where you'd probably find your lichens. Lichens are fascinating, beautiful symbioses of fungi and algae (often cyanobacteria), but they aren't invincible. They require sunlight for photosynthesis, and something to break down for nutrients, like soil. Here on the plains, we've got plenty of each. Lichens would cover the surface of the soil in a thin layer, supported by the sunlight from above and the nutrients from below. Any of the lichen forms would be possible, so there could be areas of very flat, crustose forms across one area while foliose or fruticose forms would be found in wind-blown fields elsewhere.
I'd expect most of the soil here to feel similar to our current plains soil- loamy and soft, perhaps with a harder crust of fructose or foliose lichen that would be easily broken through underfoot. In areas of harder, rocky soil, the crustose forms would dominate, feeling more like the real-world rocky mountainsides where such crustose forms grow well normally.
Real-world examples
As outlined earlier, we don't have completely fungal-dominated environments because they need a huge influx of nutrients to avoid disappearing rapidly when the food is gone. We're currently cultivating a kind of mushroom-dominated environment in the Eastern US, but I'm guessing that's not what you're hoping for. In previous eras, we had mushroom-dominated ecosystems, but don't know a lot about them. And finally, even if it isn't the dominant species in the ecosystem, the largest organism on Earth that we know of is a single, spreading fungus.
