I apologize if this is slightly incoherent, but I really need to put my thoughts out there.

TL;DR: Sirens are possessed Eridian weapons that rebelled against their creators.

The long version:

We've seen the Guardian possession in the Mysteriouslier questline, right? And we've seen how sirens are capable of interfacing with Eridian tech such as Vault Keys, even if their specific powers wouldn't allow them to? And that the powers can be passed onto someone else upon death?

My theory posits that what we know as a siren is actually a host for a semi-sentient Guardian "spirit", similar to the ones released by typical Guardians except massively beefed up. The semi-sentience would explain why, if the host is not chosen "manually", the power seems to have a preference for specific hosts: both Angel and Tannis, hosts of phaseshift, had direct access to Eridium and were somehow technologically inclined.

Sirens are able to interface with Eridian tech because they are infused with Eridian tech - sufficiently advanced magic-looking extradimensional (Phasewalk is explicitly described as using a different dimension, Eridians are implied to be not of this world due to Nekrotafeyo meaning "first landing", etc.) tech, but still.

Just like how people highly affected by Eridian influence (the Lost Legion) gain strange markings and eyes, so do siren vessels. In fact, since the Lost Legion's powers are very similar to siren powers and are empowered by eridium, this is further evidence that these powers have a similar source.

Each seems to have been made for a different purpose. Notably, the Leech's purpose was apparently to consume the lifeforce (lifeforce is 100% a real thing in this universe, just look at Eleanor's sphere absorption attack) of the entire Eridian civilization and use said power to vault the Destroyer: a redirection. In-game, the Leech is split between two vessels since they were conjoined in the womb, so instead of being able to absorb and confer energy as they please, Tyreen needs to absorb constantly and can only give back energy to Troy, and Troy can both take and give energy (anointing being the latter - it turns people into weird mystical beings, which are very analogous to Lost Legion Eternals, further proving a connection), but is generally weaker and must rely on leeching other sirens to survive.

The Seer calls sirens "acasuals", implying they somehow exist outside of causality, and carrying a disdain for them despite them being able to interact and benefit from Eridian tech. The Seer itself is a Guardian, so I think this is just implying sirens are somehow going against the established "thread of fate" Guardians are trying to uphold. My secondary theory to this is that the Eridian civilization somehow managed to control history itself, the Guardians being Eridian constructs are trying to uphold that controlled causality, and sirens are rebelled Guardians who refuse to conform to it.

As for why they're all women, I'm not sure. Maybe Eridian society was matriarchal and made their dangerous extradimensional weapons women because of that? Verdict's still not out on if Troy is trans (and siren powers go by biological sex) or Tyreen is trans (and siren powers go by gender identity), since conjoined twins are always also identical twins, so... yeah.

Again, sorry if this doesn't make much sense, but I needed to write this down somehow.

EDIT: Completely forgot that sirens canonically retain a bit of memories from the past hosts of their powers, iirc