Looking at the inquisitor more I noticed another big flaw: it has two "bad" saves and no good one. In 5e EVERY class has one "bad" save (Str, Int, Cha) and one "good" save (Dex, Con, Wis). The inquisitor as of now has no good saves, which is BAD design-wise. I understand not wanting to give them Wis/Cha for fluff, but Int/Cha is just BAD, so I suggest giving them either Dex/Cha or Con/Cha, if you want to keep with their RP of easily succumbing to vice.
Likewise, Agonizing Blast is not needed with Dark Blast if your already adding Cha to each blast, so no need for agonizing last. Also, speaking of dark Blast, there is a glitch with its write-up. You mention multiple blasts, but nowhere in its rules text do you mention how many extra blasts it gets and when it gets them. I know it's meant to act as EB, but not everybody will, so adding how it scales into its rules text is CRITICAL.
Finally, I feel if every archetype gets dark blast, that it should deal different damage types for each archetypes to keep it fitting that archetype's fluff; necrotic for healer, force or necrotic (your choice) for sorcerer and lightning for lightning.
Oh, and while this suggestion is not needed by any means, since Sith sorcerers are meant to be the best Necros I feel they should get some undead love since right now a Consular can necro better than them (due to getting higher level slots for your create undead expe) which does not seem right.
My idea to remedy this is to make two Sith sorcerery rituals you can grab with the book of ancient secrets, based on the wizard's undead thralls feature and Oathbreaker paladin's command undead channel Divinity, which I have rough suggestions below:
Command Undead -As an action, you can use your Sith Magic to bring an undead Creature you can see within 30ft under your control. It must make a Charisma saving throw against your Sith Inquisitor power save DC. On a failed save, it must obey your commands for the next 24 hours, or until you use this ritual again. Undead who's CR are equal to or greater than your Sith Inquisitor level are immune to this Ritual. You must have your Book of Shadows on hand to use this ritual. Once you use this ritual, you cannot do so again until you finish a short or long rest.
Raise Greater Undead - If you have your book of shadows on hand, you can raise more and stronger undead through Sith Magic. When you use a power that creates undead, you can increase that power's casting time to 10 minutes to have the undead it creates gain the following benefits:
- They increase their hit point maximums by your Sith Inquisitor level.
- They add your proficiency bonus to their weapon damage rolls.
Additionally, when you cast a mystic arcanum that creates undead in this way, you can expend a use of a mystic arcanum with a higher level to cast that mystic arcanum at that level instead of its normal level. (You do not also cast the mystic arcanum you expended)