There's the Archdemon and Warden mutual annihilation. And the OGB. So it seems that there is some sort of essence that intelligent, living beings have.
The first doesn't do the same for Corypheus who also has a soul, so there's clearly something wrong with the theory that it's mutual annihilation. The OGB has some kind of essence from the Old God, but again, that essence did not annihilate/supplant/merge with Kieran's "soul", so something odd is still going on there.
Also ghosts. Going to the Fade without your body. That dead mage in DA:O who you encounter when Sloth demon drags your party into the Fade - the guy was there but was already dead on the outside. I'd say existence of souls is as confirmed as can be, really.
Ghosts are never encountered, only Fade spirits re-enacting battles or emotionally strong situations. The Fade is a realm of willpower and emotion. A lot of that can remain behind without the need for a soul. We don't actually know if this has anything to do with a soul. A lot of people who were thought to be dead souls in the Fade turned out to be Fade spirits or illusions by Fade spirits. Niall may not have been dead in the real world yet, explaining why he was still in the Fade. He was dead when we woke up, but we can't say anything of before then. He may also have had his appearance taken by a spirit akin to the spirit of faith who takes on Divine Justinia's appearance.
Every occurrence of a "soul" can also be explained otherwise up until this point and some occurrences even raise massive questions because the explanations don't match what we see and experience in the games.
Actually, we don't. We can only guess what Mythal really is. She seems much too static to be just a Fade spirit, she could indeed be more akin to a ghost of whatever she was originally. My pet theory is that first elven gods were originally nature spirits (not to be confused with Fade spirits) coming from this side of the Veil, as was supposedly also the case for Lady of the Forest. That would make them "mortal beings" like forest or a mountain, or a lake, or a see, or whatever.
They could also be originally elven mages or - yes - unusual Fade Spirits but either way lore isn't clear about this.
She wandered the Fade and possessed Flemeth, she also has the same ideological shenanigans as Justice who got corrupted into Vengeance by being linked to a human. The similarities ARE there. The exact nature does not matter, the point is that she clearly has things in common with fade spirits, and thus being summoned is the simplest and most likely explanation for her shenanigans in Dragon Age 2.
Originally, I think she very much was a powerful elf, but after she became a goddess, she was at least part spirit or had a spirit bound to her, and it is that spirit that survived to bond with Flemeth.
As for the lady of the forest, she is a massive exception in the lore and will likely either be retconned into just being a Fade spirit, or she will be ignored and treated as early installment weirdness.