I'm sorry, but I completely disagree. Gary's personality is meant to be subtle and low-key in comparion to the others. Why? Because he HAS to be. His culture and home was stolen from him by the Lynxleys before he was even born. There is a clear reason why he acts the way he does.
I imagine Gary feels like he had his personality stolen from him because his whole life had been dedicated to finding ways to free his entire race from ostraciztion and separation from Zootopia. He wasn't allowed to be openly expressive like the Zebros, who are clearly privileged, rude, and are allowed to express themselves in ways Gary just isn't. I found them obnoxious.
Gary is on the run for the entire movie, and if he so much as shows ONE flaw, he knows that he could be demonized by everyone, including the main cast since he barely knows them. I only seen the movie once, only rewarching clips, and I can tell that Gary is consumed by fear that if he shows any signs of darkness, he's toast.
When you do see Gary's personality shine, you can tell that he's meant to be a clingy, soothing, sweet, considerate, curious, and playful snake. He's clearly determined to save the lizard AND snake population, even if he has to put his life on the line. But in the end, what he wants the most is a loving community. He's desperately lonely and just wants to be close to others.
As for shipping Gary with Pawbert, they do have chemistry! Gary constantly coils himself around Pawbert and is very relaxed in his presence. If you go by snake logic, Gary is VERY comfortable around Pawbert to be clinging to him so much. And they clearly make a great team considering the thorough investigation they did together at the Honeymoon Lodge.
To expand, Gary seems to show a michevious side whenever he interacts with Pawbert, like triggering his cat toy to see him act silly. Even after Pawbert's betrayal Gary keeps this up.
In one scene, Gary licks Pawbert's ear and says "daddy's busy!~" very playfully despite the very raw pain he must've been experiencing. Gary is strong willed and full of life. He has the ability to enjoy things around him, even when he's scared and treated like a criminal.
Snakes are subtle creatures. They sit and take in everything around them, but that doesn't mean they don't have personality. Mammals are naturally more loud and boisterous creatures, but that doesn't make them superior to lizards.
Zootopia 2 clearly empathizes how much anti snake propaganda there is. Snakes are evil. Venomous. Deadly. They are out to get you.
Gary wanted to be the exact opposite of that. He carries cute bandaids and a silly antidote pen to keep people safe and secure. He makes cute drawings to apologize. He's comforting and soft when Judy needed him.
Also, the dislike of hick characters seems to be your personal preference. I found Nibbles to be really refreshing. She's instinctual, clever, crafty, knowledgable, and is clearly butch coded. Her conspiracy show is hilarious and her shameless behaviour works really well with the main cast.