Snakeee, I saw matches of you vs AZ on youtube. I have some advice. Take it if you want.
At the start, you kinda gave him your piece when you ran of the stage. Diddy is like on the top of that list of the characters that you DONT want getting the pieces. They're like super bananas to him. That's probably why he started the match with the intention of just getting to them. I suggest that in this matchup on BF you should try throwing 2 of the pieces,one up and one down, to discourage him from grabbing them in fear of getting hit. if he doesnt get scared and goes for the piece (or you). you can intercept him with an attack. BF is one of the most complex stages to start the pieces with since there's many different options on how to act. I dont think giving them the piece is the way to go though.
Everytime you did a dash attack in an attempt to pick up a banana, you were countered because he knew you were gonna do it. you can pick them up without a dash attack.
When diddy did have a banana I think you were focusing more on the naner than diddy. I think AZ noticed this and baited you into grabbing them. There was a part where he stood there and pulled out a naner and you had chances to hit him (since he has lag) but jumped and picked up the naner in the air and got countered. if diddy pulls out one in the air, you can rush HIM with a uair instead of going for the naner.
when you have a naner you gotta think like a Diddy when fighting him. know their set-ups. Know how to use the banana's to make set-ups against them with mindgames. you Just threw them at him, basically giving them back to him. you NEVER want to give him his naner back. HE WANTS IT.
Dont be afraid to engage to hand to hand combat when given the chance. ZSS is blessed with a very decent up-close game when you can predict grabs and all that by utilizing her 1 frame jabs, tilts, and "dashing" mindgames. Most of what you did up-close was SH bair.
I noticed in the 2nd match he was literally rolling circles around you on Norfair.
ZSS on Norfair is can be extremely broken if you rely on aggressive pressuring game with constant spacing uairs and fairs through platforms. Diddy cant do much since he wont have time to pull out bananas. when you do that thing where you camp/ledgestall on the platforms with down b. you are GIVING HIM TIME to pull out more naners to use against you. Diddy on Norfair w/o his naners cant do much if you are staying below him on the platforms. I noticed he focused on staying on the middle platform to avoid things like this and to give him room to pull out TWO naners.
Diddy with two bananas can be a threat. if you can BAIT him into throwing them you can pick it up and use it against him. When I pick up one of them I either try to bait him into throwing another one so I could have 2 of them (she's deadly with them if used with mindgames) or I pressure with quick lasers making sure to only use them if he's not gonna counter with a naner.
And most important, you let him HAVE THE MOMENTUM. All diddy had to do when next to you was hit you with 2 naners to your shield and grab. This made you become overly defensive and doing this kept diddy at his prime with 2 bananas at his side at all times because you werent there to stop him. You can bait the naner and take them from him. If ZSS is the one running from the enemy on Norfair then there's something wrong. Once diddy has the momemtum (you'll know this if he's dribbling/playing with both of his naners), it can be difficult to get it back. That's why you wanna KEEP the momentum/pressure with you for as long as you can.
I also noticed that you tried doing things like countering airdodges with diddy near ground. his airdodge from what it seems is pretty long. instead of just trying to wait for it in the air. try a mindgame like baiting the airdodge by hitting him with a uair, he's gonna expect you to do another and airdodges, then you can FF to the ground and do a dsmash. trust me, from experience, mindgames like this work all the time.