I believe Trebol is a Logia user. I have some theories.
I know many say that a Logia user can’t be cut but we can clearly see Trebol being cut into pieces by Usopp. Trebol is not like the majority of Logia users who are made of intangible elements. Ace’s/Sabo’s Fire, Smoker’s Smoke, Borsalino’s Light are examples. You can try to cut each of those elements in real life and it does nothing. Trebol is like a jello mold. You can cut it into a hundred pieces, but it can still be returned to its original state. This is how he can be cut by normal means. Just because he is a Logia does not mean he can’t be cut. Blackbeard is a Logia and he takes double damage from attacks and when Kuzan was turned completely into ice when taking Whitebeard’s quake attack, he shattered. Just like ice would if you hit it with a hammer.
His outer coat and body is a shell made from his mucus and therefore not a true part of his body. This would provide him an extra means of protection and confuse his opponents. With his outer shell made up of mucus that is separate from his real body it would allow him to move his true mucus body freely within. So, one would never truly know where to hit. So, when Luffy struck a hole through Trebol he could’ve missed his real body entirely.
His movements in both the manga and anime are very fluid and liquid like. When he splats on the ground when talking to Baby 5 and Doffy, the way he moves his head around when talking to Robin and the Tontattas, reforming himself after Usopp’s attack and when he was defending the SMILE Factory.
Some argue that when Law attacked Trebol and cut him it proves he is a Paramecia Devil Fruit eater. Law is capable of using Busoshoku Haki. He could have used it in his weakened state to make his hit count. Though Law’s hand was severed, it was still his hand.
Trebol’s outer shell “melted” because his injury caused him to lose his focus and control over it.
I know he says Logia means nothing to him, but Trebol has had his Devil Fruit powers for 30+ years. I’d say he’s had plenty of time to create new ways of defending himself.
I believe Trebol is unique amongst Logia users like Blackbeard.