The common ancestor basically tells us who we are related to more, but does not tell you when they branched out. So we are more closely related to fungus than to almonds, and that is what we learn from the tree of life. But the common ancestor of plants was born after the common ancestor of fungus.

In Human analogy you could think of it like that cousin uncle (non native speaker, so don't know what if that is the right term) who was born after you, but in the family tree will be shown before you.

Edit: Googled a bit. I have a first cousin once removed, who was born after me (referred to as cousin uncle above)

Edit2: https://labs.minutelabs.io/Tree-of-Life-Explorer/#/?ids=ott7... Minute Earth tree of life explorer makes it easy to see this, but beware many hours can be lost down this rabbit hole.

My guess is that simosx is using the term "plant" in the strict/colloquial sense, not the either Plantae kingdom (so not including things like cyanobacteria).

We probably lack a big chunk of the whole picture. Phylogeny is based in fossils, but as most fungi are typically soft, lack of characteristic fruits or wood only a few were fossilized. Even worse, most micelia are indistinguishable from other fungi unless you pick a microscope, thus much less fossil diversity and branching is expected.