To answer your questions about the role of plant life when classifying biomes, and to clarify this point generally, I believe assigning certain biomes based on the species present in a patch is necessary, as a “biome” by definition is a type of ecological community.
I think the simplest approach is a tiered system, where simple (or low biodiversity, low-tier) biomes are assigned based only on patch stats like precipitation and temperature, and more advanced (biodiverse, high-tier) biomes can later be assigned based on the emergence of certain kinds of species.
This may remind you of Spore’s tier system for planet terraforming, which is meant to convey similar concepts.
In T0, before life exists on land, there are only patches of Barrens (not a scientific term), with whatever temperature and precipitation (or other stats) they happen to have.
In T1 the land has experienced primary succession, making land biomes relevant, and Barrens patches get assigned a biome based on their stats. At this early stage, forests and scrublands are not yet possible, so we only have Deserts and Wetlands (which can be defined purely by precipitation/humidity).
In T2 “shrub” organisms have evolved, and scrubland biomes become possible, which are populated in patches with the appropriate stats and presence of the right species.
In T3 “trees” have evolved, and the same occurs with forests.
This does mean we need to define what makes an organism a “shrub” or “tree”, which is a whole other discussion. I am assuming we can arrive at such a definition and thresholds for how many “trees” make a patch a forest, etc.
I think this approach is fairly intuitive and compelling. It means if there is a mass extinction, or deforestation, the simple lack of “trees” that got destroyed will change the biome, just as would happen in real life. A healthy and complex ecosphere will have many different biomes, and a young or struggling ecosphere will have fewer.
Biome types may be pre-defined, but biomes naturally emerge from the simulated climate, terrain, and species which have evolved there, leading to infinite variability.