His DD is for sure one of the weaker ones in the game
I would agree that it's slightly subpar, but mostly because his options out of it are relatively limited. He has the longest dash->run time in the game, and his dash speed limits the potential of his pivot game. Pivot jabs/tilts are still a good, if underused, option.
I'm not defining poor shield pressure as anything worse than spacies' shield pressure, but it should be put into perspective with other characters.
Okay.
All of Mewtwo's aerials sans nair are positive on block when HC'd. Nair is -5 on weak hits and -2 on the final hitbox. Non-HC nair is -9 on block but can autocancel out of a short hop, bringing it back to -2. Fair is -0, uair is -3, bair is -7, dair -0. There is a bug regarding the use of multiple aerials during hover, but the PMDT is aware of this and it's generally not
too significant in the meantime.
Jab1 is -5 on block, dtilt is -10. Both have good range and slight disjoint.
Think of it like Peach's shield pressure. There are limits to how long she can keep any part of it going, but while it's going it's safe enough that you have to respect it. When you mix up what you're doing and how you keep it going, it's rather effective.
Of course movement and aerials are part of neutral. I'd have thought that would've gone without saying.
I could say the same of grabs.
But Mewtwo tends to start his conversions (in most situations) off of the moves I listed.
Shadow Ball doesn't start conversions, it finishes them. Ftilt is a spacing/get off me poke that can set up edgeguard situations. Uthrow is only an effective combo tool against fastfallers, the percent range in which it works is limited, and on the higher end of that range you can only follow up if you use teleport. It'll kill eventually, sure, but he has better options. If you kill with uthrow, they lived too long on that stock. Dthrow techchases fast and mid-fallers, but his techchase game is somewhat limited. Against floaties it's basically just position/damage. Think of it as a higher damage, somewhat laggy version of Marth's fthrow. Fthrow/bthrow are obviously positional. His command grab is his only consistently rewarding grab option, though the risk in using it is balanced accordingly.
Meanwhile there was no mention of jab1, fair, nair, or uair, all of which are solid options for conversions. Even utilt, which is decently rewarding but not exactly safe, arguably deserves a mention over ftilt or Shadow Ball.
How I see hover is that it's mostly only good to pressure shield or punish endlag since it's a risky option.
You can put out an HC aerial with just 9-10 frames of total airtime if your execution is on point. Learning to use hover in ways that minimize the risk of trades is part of the gig with Mewtwo.
About the approach: I think it's pretty unreasonable to discount the importance of approaching entirely.
Moreso that the concepts and thought processes usually attached to the word "approaching" don't really have a place in Smash. Fox for example, since you brought him up: his strength lies in his ability to 1) conditionally avoid engagement while forcing the opponent into action and 2) punish errors with a high degree of efficiency thanks to highly effective pressure and rewarding combo options.
Mewtwo plays a mixture of pressure and punishment while using his own positioning options to play around the opponent's attempts at advancing their own gameplan. When examined from this viewpoint, you'll find that Mewtwo certainly has varied and flexible tools to work with.
I'd be much obliged if you were to explain exactly why Mewtwo goes even with Fox. I don't need to hear about Mewtwo's punishes and edgeguards because I already get that aspect, but an explanation of how Mewtwo answers Fox stuff overall would be appreciated as I haven't actually used Mewtwo against a real Fox, and only in friendlies.
1FD has the right idea. A large part of the skew in the Peach v Fox matchup is Fox's superior mobility and ability to laser camp the hell out of her given the opportunity. That advantage is greatly reduced against Mewtwo thanks to his faster, albeit more committed, mobility options. His coverage is a little different with changes in frame data/range/hitbox placement and properties, but combined with his movement options you have the general pressure/punishment/positioning concept I described above.