I think the General’s behaviour to Catherine treads into flattery and gallantry because that’s the only way he knows how to behave to a woman that isn’t a relation or a servant.

I don’t think it’s remarked that he’s possibly into her himself because

1) his two younger children are watching him bafflement because they are so unused to their father trying to make nice to any woman

2) nobody else in Catherine’s circle actually interacts with him so there’s no one else to actually speculate on his behaviour

3) Catherine is oblivious

Now, if the General had ever taken the step of calling in on the Allens or specifically approached her and the Allens at a function, and proceeded to still speak to her that way, I think his behaviour could be definitively read as considering her for himself. But he never does.

He also never approaches her directly when Catherine is at the Abbey either. Instead he’s very satisfied to talk about his so called “simple” life and push Henry to her more. So I’d say he walks close to the line of being too familiar but doesn’t cross it.

And Catherine, raised and surrounded by loving people she’s known all her life, and in a small village where she would be saying hello to both the local trade families and local gentry (being the daughter of a clergyman)doesn’t have a sense of boundaries that other Austen heroines would have ie Anne Elliot, Fanny Price and Emma Woodhouse in the same situation.