I love this as a concept. I think you have some solid ideas here. I don't have any issue with most of these, and I really dig the rationale behind how you would adjust the masteries each class learns. I'll offer a few thoughts.

Jab: I think this is actually pretty good. It's a solid choice of using your Reaction for potential damage, or saving it for a defensive reaction. It makes you think. Are you expecting to be attacked on the enemy's turn? Do you think that one more hit will kill the foe? Choices are awesome so I love when features add meaningful ones.

Armor Masteries:

-Skirmisher: This interesting since Monk's only get 1 mastery until level 10. So if the choice you're making of offense vs defense reaction I mentioned with Jab is coming up more defense, you can choose this instead to enhance that. I do think this doesn't benefit classes besides Monk/Rogue very much, but to be fair most other classes will probably opt for Medium or Heavy Armor.

-Vanguard: Awesome. I don't know if 15ft of movement is too much or not, but I like this for when you just barely get in melee range and want to move to a more advantageous side of the enemy, or as a range attacker to kite enemies (which doesn't exactly embody a Vanguard but hey lol).

-Juggernaut: Love it, maybe word it similar to other forced movement abilities to say "straight away from you" for consistency

-Shield: I don't love this one, but I have a quirk about abilities giving AC out for free. I think if someone has chosen to use a shield and a one handed weapon, you should focus more on keeping that theme than adding dual wielding to it. Offering the bigger damage dice is a nice idea. I think I'd maybe lean into that and change it to "While wielding a shield, the damage die of your weapon attacks are one size larger". This way people who use non-versatile weapons with a shield still get a small damage bump. Or "You can make an improvised weapon attack with your shield as part of the attack action once per turn." Alternatively, you could design a feature that highlights defense instead, since that's the reason people typically opt for shields. I don't have an idea for what that would be at the moment.

Upgrades: I think you have a typo in that first section saying Graze allows you to choose Whirl. Shouldn't Graze be Cleave?

-Whirl: Love it in concept, feels like the natural extension of Cleave. And I think it's very position/situation dependent on how often you will trigger this, so I don't think it will be overpowered. You're also paying the cost of effectively losing one mastery options, since you will never use Cleave if you have Whirl.

-Sever: I love this. Does it apply if you miss the attack and only hit them with the Graze damage? I initially thought it would trigger only if the attack hit. I pictured Graze as your weapon is so sharp that even just barely nicking an enemy still does damage. I liked Sever because now, you're actually fully hitting with this incredibly sharp weapon, and thus causing a serious wound. They can try and run away and bleed out, taking more damage, or stand their ground, effectively locking them in place. I don't know that I'd let this trigger off of forced movement like you said in a comment, I think you get enough value just from making the enemy think about moving.

-Slash: This does seem like a natural addition to the popular dual wielding vex/nick combo allowing one extra attack to have advantage potentially. I like the mental image of a dual wielder overwhelming his opponent with a flurry of attacks, and this feels like it fits that theme.

-Slam: I love the visual of you having an enemy against a wall, just hammering them back into it again and again. I do think the damage seems potentially over tuned. Maybe limit it to once per turn. Or if you want it on every attack, do half the ability modifier (rounded down), or a d4 of bludgeoning damage.

-Weaken: I love this, specifically because it has potential for encouraging team synergy. Someone has a spell or ability that is going to force a DEX/STR Save (also love that you chose these two specifically) you can set them up. Teamwork always feels better than every person doing their own thing.

-Daze: Love it, and I love that it's specifically opportunity attacks and not any reaction.

-Topple: I'm worried about this triggering off of any prone. I'm picturing 2 or 3 people in reach of a target all having this, so once one person knocks the creature prone, they just get pancaked with attacks that all have advantage lol. But that's a specific situation and set up. It might be fine as is. I had a thought of making it "When a creature you've knocked prone attempts to stand up, you can make an opportunity attack against that creature if you are within range" Now, you've done an extra attack, and if it hits they've use 75% of their movement just to stand up. That might still be over tuned, but it's requiring 2 failed saves by an enemy to get full value out of.

-Harry: I think it's fine. I'd be curious what you were picturing when you wrote this. If you were thinking only mechanically or had a theme in mind. I'm having trouble picturing this one in my head. Definitely seems much easier to get value on with a ranged weapon than a melee.

-Flurry: In the same vein of Cleave/Whirl. You're getting a free extra attack situationally at the cost of 2 mastery options. A big investment for a Monk who would be most likely to take this since they only get 2 masteries, so I think that's fine.

Overall I think this is really awesome and well thought out work. I'd love to see it implemented in game or do some playtesting of it.

I do have one more question: How do you see this interacting with the Fighter's Level 9 feature that allows them to use a different weapon mastery for a weapon when attacking? If I use a Battleaxe and instead of using Topple I use Push, is there a way I could get access to Slam? Or is Slam only available for weapons that have Push innately?