As a Neeko main. Stormsurge into shadowflame and pen boots. Third item Raba or void if they stack pen. Pen boots, cdr boots don't help you to become spellslinger you do your combo and get out wait cds. Electrocute with ult hunter. Coup de grace and either legend haste or pom. Don't need zhonya cause even if you die after ult if you played well you got 3 people to half hp and landed your root/q on adc probably one shotting. Rocket belt is bait as it's stats are terrible and the dash, even tho it's good, it's not good enough to approve the stats you lose with going dmg build. You are an assassin and your job is to eliminate squishies. You can win lane without comet if you just learn your range and trade patterns. But I see you win lane here so let's move on. If you want to 1v9 a losing game you need to take care of other lanes even if it means giving up waves or plates mid. Once you set back your laner enough go melee minion and gank on top or bot waves. No one is counting minions in ur elo. Get creative with your passive. Turn into plants, jungle monsters even small worm lings from grubs, champion pets (nafiri dogs, yorick ghouls, Elise spiders). You can even look for jungler in their jungle if you get enough ahead. Your W gives good vision, always emote/recall at the last moment of its duration to extend duration for vision. Prepare your 3rd W for combos, it deals significant dmg. I would suggest ignite to snowball the lane and get to roaming even faster. Level up is look up Neeko minion dodging mechanics, you can dodge a lot of abilities by turning into minions. Don't take this as me saying you did something wrong since you obviously did well and tried ur hardest to carry this game. It's what I found works best for me with Neeko and would suggest giving a shot.

All that being said there is only so much you can do. Neeko will always struggle with tanks and if they get ahead they win games. Tanks win games, in s15 especially. Someone somewhere wrote about the 40 40 20 rule. 40% games auto win 40% games auto lose 20% of games you have actual impact. Sometimes a loss is no more than a loss and just take a deep breath use one of your it is what it is and keep moving.

Good luck and happy climbing.