I have consistently said that cat guardians should respect their cat companion as a feline but treat them as a member of the human family. I think that is the right combination but it does lend itself towards anthropomorphising your cat. However, I don’t think this is a bad thing necessarily. The experts say you should not anthropomorphise your cat because it can lead to problems.
For example, if you think your cat is a human baby you might pick her up like a baby and cradle her in your arms, belly up. This is not a great way to hold a cat. Some cats don’t minded but others will because they feel vulnerable. It’s just one minor example.

The baby-faced, owl-like face of the Scottish Fold kitten above taps into the anthropomorphisation of cats. It encourages it and arguably this breed of cat was developed to use the attractiveness of a flattened-ears cat to prospective purchasers.
Another, perhaps more important example, would be about expectations. I have always referred to expectation management in cat guardianship. It’s important to expect a cat to behave like a cat and not a little person in order to avoid disappointment which can lead to a strain in the human-cat relationship. It can even lead to punishing a cat for bad behavior when in fact it is natural feline behavior and cats don’t understand punishment (try divine intervention instead if you must).
So, you don’t want your cat to jump onto the kitchen counter because people don’t do that and neither should cats. You don’t like your cat jumping up onto other objects which is entirely natural for a cat but highly unusual and unnatural for a child! I’m just making a point about the differences in behaviour between cats and children. If you expect a cat to behave as a toddler you’ll be disappointed. Therefore it can be a bad thing to anthropomorphise your domestic cat companion.
On the other hand it can be a good thing because it means affording your cat equal rights in the family. Your cat has enhanced rights equivalent to human rights. This should lead to better welfare through improved caretaking. Examples of where this might become evident is in providing the highest possible food and doing your best to allow your cat to express her natural desires and motivations. This means allowing freedoms consistent with safety and security. It means providing objects to climb as cats, as you know, love to climb and are very good at it. They live vertically as well as horizontally. Or building a catio.
Ironically, giving a cat enhanced animal rights, equivalent to human rights, leads to respecting the cat as a cat in my examples above. So it is not altogether a bad thing to anthropomorphise (humanise) your cat companion. It’s a question of keeping expectations in check and always reminding yourself that you’re cute friend is a whisker away from their wild cat inheritance.
It is said that domestic cats are barely domesticated while the domestic dog is thoroughly domesticated. This impacts the relationship because in interacting with a domestic cat the response will be feline when sometimes the human guardian expects a human response.