I don't feel like Mewtwo has approach or space control options that are on the same level as characters such as Fox, Lucas, Marth, Roy, Ike, Wolf, and some others.
Perhaps not. He is certainly not Wavedash into Dtilt: The Character, though I once made the error of saying so many months ago. That was Melee, this is PM. His kit works more like a puzzle of overlapping pieces, one that nobody's quite finished putting together yet. Nuanced. It's fun. He can still cover a lot of options though, the way he does it is just a little different. Think of the way Peach covers herself with hitboxes and uses that threat to control the space around her. Think of the way Luigi zips around, keeping you on your toes, staying safe by constantly moving in and out and around you.
Now imagine they have a baby and Marth gives it a sword on its 18th birthday. What would it do?
Speak softly and carry a big ol' tail-sword. It's also psychic because reasons.
Rapid, varied movement in and out of threat zones mixed with good range, pseudo-disjoint, and coverage in all directions is a potent combination.
There are answers, but remember how fast Mewtwo can transition in and out of pressure. Wavedash covers a lot of ground, wavedash into hover with momentum covers more. His waveland needs help though, it's actually worse than his wavedash much of the time due to ECB nonsense. 5 frames landing lag on an HC aerial. He can waveland out of sh bair and uair, or do a second bair if he so pleases, or follow with a hover/HC aerial, etc. Teleport can get him out in a pinch. His weakness here is arguably in how much space he tends to give up if he is forced to retreat rather than doing so on his own terms.
Again, it's not all about directly approaching. Mewtwo wants you off balance, uncertain, whether that results in overcommitment or retreat. Either is fine by him. He doesn't have to force his way in. He only fully commits when the opportunity presents itself. Even so, it's true that neutral can be a struggle against some characters.
Let's talk about short hop nair, since you picked that one out. You don't just raw approach with it, it's a 41 frame move that covers a very specific space with weak repeating hitboxes. What that doesn't tell you though is that instant nair can autocancel starting the frame after the final hitbox terminates and that his short hop lasts
just long enough to reach this frame, giving you shield pressure equivalent to a late HC nair (HCing early prevents the final 4% hitbox from coming out). Suddenly it's rather effective against an opponent in a defensive position, as are properly applied hover (followup fair/waveland/nair again/command grab/etc) and HC nair (timing mixups!) in the same situation. Short hop nair just doesn't burn your double jump and as I said, it's relatively simple.
Jab is frame 8, yes. I've been pushing the idea of moving it up to frame 6 (with compensated IASA) for that very reason. Slightly too slow for the hole it wants to fill in his kit. Still decent, just not quite what it needs to be. Maybe frame 5, but not any faster than that.
And I've only mentioned what he does once he's in your space. I haven't said anything about how he gets there in the first place, or what he's doing to bait you in return.
To be clear, I'm not yet convinced that Mewtwo is as good as Nausicaa seems to think. He could be, different perspectives and all that. I do think he's really good and generally underrated, and I'm still uncovering new things on a regular basis despite inconsistent playtime. So much of his kit is untapped or simply misunderstood.