It doesn’t really make sense to look at a species that’s alive today and think of it as the last common ancestor of two branches, because that species has been changing as well (even if not very much).

Plus, given we don’t have chloroplasts but the Euglena does, it might be safe to assume it split off the branch that would eventually form plants after we did. Unless we once had chloroplasts but got rid of them, but I haven’t heard that theory.

But it seems as though the Euglena split off quite early, yes.

It is thought that euglena split off from the plant/green algae line before the development chloroplasts from captured Cyanobacteria. It likely that Euglena’s ancestors received their chloroplasts from engulfing an eukaryotic green algae. Over time, the engulfed algae was reduced to a chloroplast and a nucleus, thus serving a similar function to the original chloroplasts.