Yep, you've got the gist of it. There are numerous angels and demons available for contracting, many with unique and varied powers like the examples you mentioned. Funnily enough, you managed to hit on the exact two powers that have lore relevance to this story. One of the seven Ascended demigods possesses the power to reverse time by a limited amount, while it was a war against a Void demigod (shapeshifter type) that ultimately drove Regret to ascend. So yeah, there's absolutely all kinds of demigod spirits to contract with.

What makes Ascendants like Regret stand out from all the rest is that they are the only ones with mortal forms. As such, Regret is the only demigod you can contract with whom you can actually see in person with your own eyes.