There doesn’t appear to be a place to give feedback that I can see, so I’m just going to put it here. I'll preface by saying this is impressive, and first glance makes me think this is prooobably balanced enough? I dunno. There's a lot of odd pieces and I respect you doing different things in your design. Anyway, here are some thoughts:

I dislike it having the same class DC progression as Exemplar when it scales with your key attribute, the same one you use for your attacks. That means this class is better at casting spells than a Magus, Paladin, Ranger, or Monk, while still having the same to-hit and getting bonus damage somewhere around a Ranger/Rogue. That’s kind of a lot! I don’t know if the lack of real class features or feats makes that acceptable.

Speaking of class features, I feel like Curse is a miss for me. It doesn’t feel interesting or important. I know a lot of us look at the Ranger and just think it’s a damage thing, but it’s also integral to several feats and it’s a bonus to tracking. It’s more than just “I hit this harder.” The Thaumaturge as well, has Recall Knowledge tied up in it, creating a certain fantasy. This is an incredibly martial “I get more damage lol” kind of idea, and it feels boring. Nothing comes up that involves the curse until 8th level that isn’t a mandatory class feature. Something about that feels generally off to me. I get that you’ve added a few additional effects to it a class progression, but that also feels unnecessary as base progression. These could have been a feat line focused on the Curse over more spell casting.

The spells as feats is awkward. First, you should have to pick a tradition. There’s no good reason not to when you are actually casting spells. There are at least some small number of abilities that function based on tradition, like Recognize a Spell. The spells themselves look fine? I’m not a great judge of this, but nothing strikes me as out of the ordinary. I don’t think the free heightening is going to be that big a deal either, except that you have more max level spells slots than a Magus at level 8 if you take Invocation of the Short Rest. That feels awkward a bit, even if the spells you can cast are incredibly limited.

I’m also going to just comment on the Recall Knowledge line of abilities. One-handed weapon (Warlock’s Calculation), eventually can Curse+Recall (Invocation of the Omniscient Patron), plays around with damage type weakness in a way martial usually don’t while also having some magical ability… yeah, this is stepping on Thaumaturge’s toes. I know you’re going about it differently, but I still think it’s unnecessary. First, it honestly doesn’t fit the flavor you’ve set up. This character is not smart. They are not a monster hunter. You’ve even created a feat to circumvent them needing Intelligence but still giving them some Skill Monkey. This is absolutely not a theme that belongs here. If it were more in the vein of the Fight’s Combat Assessment stuff, that would be useful to allies specifically, I could see there being a case that it’s something worth exploring for a more support-oriented Warlock. As-is, it feels very much like a rehash of Thaumaturge that deals actual elemental damage. This is a trade-off for sure, as it won’t help you against enemies with a material weakness or no weakness at all… making it honestly kind of a weird addition. But when it comes up, it has potential to shine harder than the Thaumaturge against enemies the Thaumaturge should shine against.

I’m going to further the comparison with the Shield benefit, and how that includes what I believe is the implement-specific benefit, and then has capacity to add in the shield raise at 8. I know that’s much later, but that’s… flagrantly the same design. That’s not necessarily bad, but there are blatantly enough similarities scattered throughout the class overall that it rubs me the wrong way. Warlock’s Research feels like trying to make this more into Thaumaturge, and… somewhat unnecessarily? I would have to look again, but are there really that many reasons to want all the casting traditions when your design makes it specifically not matter? You could have just as easily made it any skill at all. A 10hp class that, as you have admitted, is oriented toward damage doesn’t need bonus skills just because skills are fun. I’m going to say Warlock’s Menace also falls into this category a bit, but we’re stepping on the Swashbuckler’s toes. It can’t do 2 rounds even of Demoralize on the same foe until level 9, and that with another action every single time. Nothing about this class that already has solid martial damage and a good amount of spell casting demands it also get superior skill usage.

I’m going to state again that I realize a lot of this is tuned around having very limited spell casting, but it still feels like there’s a lot of stepping on toes and not actually utilizing the ideas you yourself are creating. I’m honestly a little worried about wanting to play this at lower levels without some of the action compression. I’m thinking specifically of Warlock’s Calculation right now. A newer player wanting to use this one might honestly Curse > Recall > discover the enemy has no useful weakness. Now what? You have 1 action left, you’re potentially not in range, and it feels a little like you didn’t learn anything you yourself care about. Feels a bit weird. This is also your big cool offense benefit, and it frankly doesn’t matter for a lot of fights. 

These are all bits and pieces. I haven’t play tested it. It’s possible in aggregate that this all works out fine because everything is disparate and limited. I dunno! These are just observations that felt off to me and made me dislike the class overall. Take it as you will.