I've gotten to play this matchup more recently (Hungrybox and Fearless at CEO and my primary training partner picking up Puff) and the more I play it the more fun I find it. Bair footsies can be like a bout of trench warfare, trying to place a move in just the right spot. Luigi can gain the upper hand in these exchanges with his significantly better mobility on the ground and SHAWLs. Like I said before, usmash is your best friend and you can take advantage of its invincibility frames if Puff is coming in high. When Puff bairs your shield, fades away, and comes back with another bair, that second bair will be higher due to the way his aerial mobilIty works--you can punish it with a wavedash OOS usmash before it comes in and after it hits your shield.
Dthrow can lead into good combos and kills but it can also be DIed. At medium percents, dthrow from a side platform can put Puff just above the top platform, potentially leaving an opening for usmash or ping off the top platform.
Fireballs are actually an effective way of both keeping Puff away and limiting his options offensively and defensively. Shoot a high fireball and Puff has to come in low, grounded fireball and Puff might shield, et cetera. This is something that adapting to your opponent's movement patterns and recognizing OOS habits will get you much more mileage out of due by presenting you with opportunities to more precisely limit the options that they probably want to do. (This is good skill in general, and I think consciously implementing something into your game in a particular situation helps you understand that concept more thoroughly so you can apply it to any situation you want to. This works for me, at least.) Be careful that you're not too close to your opponent when you shoot your fireball, it's very punishable at close range.
Watch out for your opponent trying to take advantage of your beautiful wavedash and crouching. Luigi can't grab a crouching Puff which will lead to a free punish, or if you try to come in with a dsmash or something, you'll get crouch cancel rested which makes you feel like the biggest noob in the world.
Where Puff really beats Luigi in this matchup is off stage. Puff can easily deal with Luigi's recovery horizontally and if you're below the stage. Always try your best to recover as high as possible versus Puff. His limited vertical mobility and poor upward hitboxes allow Luigi to for almost free if you cover yourself smartly with a dair. Once you establish this threat your recovery options open up a little bit more. Puff can easily rest a missile on stage so make sure you hit any edge cancels properly.
To edgeguard Puff is difficult but certainly not impossible. Threaten high recoveries with fireballs and bairs, punish low recoveries with ledge invincible bairs, and you can punish missed sweetspots with backwards dairs on the ledge. If you land the meteor hitbox Puff is dead almost certainly. When Puff is trying to get off the ledge I like to SHFFL fairs, which Luigi can actually do quite exceptionally; his floatiness gives you a lot of control over the timing and spacing of your aerial.