**English aint my first language so dont be harsh on this post**
Hi there, my style of playing is a bit different than yours so you may not agree with some of my suggestions. I would tell you my opinions on what i would do and what skills or movements you are not implementing in your game that I believe would help you improve and mixup your style.
Alright then, I saw the first game and my opinion was, well this fox is not really that good, your puff is doing lots full hop (or dobble hop) slow drop nairs (witout fastfall every time) and fox is trying to contest him in the air, where its loosing the trades mosts of the time, I guess if it keeps working you can keep doing it... yet in the 2nd and 3rd match he realize it and start playing a more ground game and waiting for your landing, he kills you about every stock with either a usmash and or jab to usmash.
Usually this is how most of the fox that knows the matchup plays: they first start lassering so you are forced to approach, when you aproach past their perception of "safezone" (bassicaly the zone where you cant hit them before they are able to react), if you have played puff for sometime you know what im talking about. After you pass this zone, this is where the game gets tricky, they can either a) jump at you with a an attack (fullhop overshooting nair, short hop nair or dair to grab/jab).
b) Jump over you, get to the high platform and either drop with an aerial or just run back to the other side of the stage and reset the distance, forcing you to overcommit trying to read their following movements, and this is usually where the good foxes takes advantage and punish or read my overcommitment.
c) if you are fullhopping and trying to cover the platforms, they can either run past you on the ground and bair behind you, or also staying grounded wait for your landing expecting to usmash or jab or grab any of your different options.
Also most good fox, when you are around 50-70% depending on the stage, they will rather shark for grabs rather than usmash since is safer.
there should be always an optiong that you can do that beats theirs, but puff has the short end in the exchanges, and allowing fox to take low risk, high rewards options against you make his game alot safer. Its a constant rock paper sissors where the "ties" usually end up slighly hurting puff more.
Now my point is, after you get to a certain level, improving your techskills becomes less important, and knowing what your oponnent options and predict his intentions start becoming a more valuable skill. What I mean, look at your video from the fox point of view and start preddicting what would you (fox) do in every situation... you can smell him sharking for usmash, you can predict it when you are in neutral deciding what your next move will be. After knowing so, you should first be sure to throw safe moves that wont be punished by the usmash, and even better, bait for it and punish accordingly (you can shield to rest pretty easy with just a little practice, or if you dont feel confident, you can just grab/ bair them. **remember to be aware of they being able to crouchcancel your aerials in some cases.
My next advise would be to improve your ground game, or aerial game close to the ground. I didnt saw a single wavedash OOS in the hole set, and believe me, its the N.1 way to get out of shield preasure for puff. If you havent master this yet, you should make this techskill a priority. Try getting 20xx 3.05 and make fox/falco do their shieldpreasure command. And practice getting wavedash oos right after they shine, you will get tons of fsmashes after the wavedash if they dont have lots experience with that. Another improvement could be to shorthop and bair on the max safe range you can infront of their face, correctly spaced its nearly imposible to punish unless they fullhop and commit to overshoot where you would land.
Also you should use more fastfalling, on your aerials, it gives less time to get under you so they can set up their usmash, also it helps you to mixup you speed, throwing them off. I can see you are confortable using autocancelled aerials, so you should figure out the height where you can throw them with fastfall so they still autocancel themselves (I supposed you have no problem Lcanceling your moves on other scenarios). Remember, try to be as unpredictable as posible, mixing up no fastfall, fastfall, autocancelable aerials and lcancel last minute aerials (always trying to stay safe). Didnt saw any dair to grab on the hole match and believe is really usefull against everycharacter (remember the more % they have, the more likely is that it will connect because of the dair hitstun, so try using it after 60-70% so it comboes to grab).
The last advice I can give you after watching the match was you way of edgeguarding. I like you how you dealt with the fox when they tryied high recovery (either upb or sideb over the height of the stage) even when you missed some of them. But you need ot work on what to do when fox is under the stage, since they can only upb so they should be around 80-90% dead. You can practice with a lvl1 cpu and just throw them out, they will always up under the stage. Just that they wont sweetspot, so dont expect to fsmash them everytime. Try going out and fair, or grab the stage so you get invincible frames and fair/bair them.
If you see you wont make it in time you can always dair on the ledge to reset the position and give you another shot to edgeguard.