Mixing Korean and Thai BL could be an interesting road to follow, mixing Thai drama with Korean clean execution - could work. But this just doesnt.

The story as it is laid out felt promising: aloof celebrity with trauma and abandonment issues, a rich dad in the background, cute dog-loving poor Café-owner, a Vet, ruthless moral-less filmcrew... But the story as it progresses does nothing with it and it is frustrating and annoying without a satisfactory outcome. Was there supposed to be a second season? So many plotlines go nowhere, eg. the secretary (?) with the reporter or the relationship with the father.
The aloof Uno because of past trauma with a dog (and I don't believe the justification for that trauma is enough for that kind of longterm issue with it) is afraid of dogs. And then he spends just a day with one and everything is great! Come on, there was so much potential of slowly resolving that problem with the help of his future love interest. As it is, they fall in love inexclicably and far to quickly, I did not see any sparks. He is just mildly interested in the trauma-thing and mistrusts him (rightly so) and suddenly they are in love.
Some scenes make no sense considering they know they are being filmed. Granted, they think they are save after 9 pm, but that would need some prompter like checking the time. Uno doesnt seem the type to devulge past heartbreak just like that. The story with the Ex-boyfriend that is supposed to be the reason for the café owners introverted character is like an afterthought. It lacks detail and integration to make it convincing.
The sets are a laugh. The so-called dog café is clearly an empty commercial building and no one bothered to decorate. Couldn't they find someone to sit aroud drinking coffee? No surprise that enterprise is close to going bancrupt, no atmosphere, no costumers AND no dogs! That is just lazy filming.

The treatment of the dog, both in reality as well as in fiction is questionable. In several scenes, the sheperd is obviously uncomfortable and does not want to be there. In fiction, they stress multible times that the dog is in constant serious pain - and then they pull him around another whole day for their egoistical I-dont-want-to-say-goodbye-yet feeling. It rally bothered me to think that during the Bonding-Moment in the sidecar the dog is really suffering every minute. Love for the animal would have been to make the hard choice quickly - as the vet and the dog-lover should know.

Acting is a bit weird due to the language barrier. You have to look past the very improbable trope, that several people can perfectly understand the other language but not be able to speak any of it. In Unos case that makes no sense, he was abandoned by his father when young and he grew up in Thailand. Where and why would he have learned Korean that well? But well, that is how ist was set up.

I dont get the relevance of the title, I dont think Uno is cat-like at all.