I'm curious where you see Delgado in Missy? To me one is sane, a gentleman, even polite to Miss Grant. Missy is batshit crazy, thinks that giving the Doctor a Cyberman army is actually a /good/ idea, and certainly doesn't have the companion rapport with Clara that Delgado did. They're just too different to me.
It really depends on how you look at it.
Michelle Gomez’s mannerisms, expressions, and delivery are often similar to Delgado’s—she can pull the exact same sneer—but it’s more than that. There’s her semi-friendly attitude towards the Doctor, mirroring Delgado and Three’s fairly amiable relationship. There’s her concern for the Doctor, which Delgado frequently displayed. And yes, there’s politeness.
Delgado will always be the best at the whole charm thing—he was capable of murdering people and being impeccably polite about it—but it’s a trait most of the Masters have shared, and Missy is no exception. She invites Clara over for tea while holding the world’s planes hostage and politely asks about her boyfriend, knowing full well he’s dead. That’s exactly the kind of thing Delgado would do (I think an underrated part of Delgado!Master’s character is his sense of humour—the “he sat in this chair and just slipped away” line of in Terror of the Autons kills me every time). Like Delgado, Missy calls everyone “my dear” and generally speaks to people in a civil manner. She just has a tendency to suddenly switch to her “bananas” side, which isn’t my preferred thing, but I’m pretty sure it’s a calculated act on her part to throw people off balance. It’s not something Delgado would do, because he’s very invested in the gentlemanly image he presents, but a lot has happened to the Master since Delgado which has caused them to shed that image to a certain extent.
You’ll notice, though, that Missy does try to present a similar image at times, except she plays the role of the old-fashioned lady rather than the old-fashioned gentleman, and she’s more willing to toss the facade aside when it suits her.
As for the Cyberman army gift, it may seem like a weird thing for a supervillain to do, and if taking over the universe was the Master’s only motive, it would be completely out of character, but there’s more to the Master than that. They want the Doctor to acknowledge that they’re right, and that’s exactly what accepting the army would mean. It would be the Doctor agreeing that yes, the Master was right—conquering the universe is the best way to get what you want, and the Master knew it all along and the Doctor was wrong. When she kneels to him in the graveyard scene, it isn’t a gesture of submission, because if he accepts power over anyone—including her—it proves she was right and puts her in control of the situation, because he’d be doing exactly what she wanted.
The Master has always needed the Doctor’s approval to a certain extent, which is why they felt this scheme was necessary. They need the Doctor to acknowledge that they really are superior, and they need the Doctor to admit he was wrong and should’ve joined them from the start. The whole thing was about forcing the Doctor’s hand. If he accepted the army, the Master won, and if he refused, the Cybermen would kill all the Doctor’s precious humans and the Master would still win.
So how is all that like Delgado? Well, I rewatched Colony in Space yesterday, and I can see a clear parallel there. After the Doctor guides the Master to the Primitive city, the Master has no further use for him, but he keeps him around anyway and then offers him joint rulership of the universe. There is absolutely no reason the Master needs to do this. He isn’t the Doctor’s prisoner, trying to bargain a way out. He’s already in control and could kill the Doctor at any time. But he still tries to convince the Doctor to join him, and simply cannot understand the Doctor’s refusal. He offers the Doctor the exact same thing Missy offers him: the chance to help people. All the Doctor has to do is accept that the Master is right and that using the superweapon to conquer the universe would be in everyone’s best interests. It’s a very similar scenario to Death in Heaven.
You mention Delgado’s relationship with Jo vs. Missy’s relationship with Clara, but it’s important to note that the Master/Jo relationship is pretty much unique. Most other companions absolutely despise the Master. Jo is the only one who really comes to close to getting along with him, and Clara actually comes closer than others like Tegan and Martha do.
Basically, if you focus on the “batshit crazy” parts of Missy’s personality, then it’s easy to say she isn’t much like Delgado, but she has plenty of calmer moments filled with cold, calculated evil, and she can turn on the politeness when it suits her. I would also argue that Delgado has a lighter, zanier side, which often gets overlooked. There’s his sense of humour, which I already mentioned, plus other things like murdering people with daffodils, having way too much fun as a cult leader/vicar (including reciting Mary had a little lamb backwards to summon a demon), watching The Clangers, using ridiculous aliases, and taking people calling him evil as a compliment. He’s more reserved than later Masters, certainly, but he enjoyed himself immensely in his evil escapades.