Right now, the Falconer’s hawk feels too detached from the character, something more akin to a random disposable summoned minion rather than a loyal, persistent sidekick. The bird is totally absent while in-town, and out in the world it is frequently flying around or fighting off-screen. You push a button and your bird may blur across your field of vision, but it struggles to feel like an extension of the character rather than just another button you push. The Mastery does not feel distinct enough from the core class, which is unfortunate since it’s a really cool concept on paper and the gameplay is fun! The bird needs to feel present and engaged more than it currently does.
My suggestion is to have the hawk recalled to the glove while in-town and/or when not fighting, to better emphasise that dynamic. However, any small changes to make the bird feel like a true extension of the class you’re playing rather than just another ability on your bar would be really good at solidifying the Mastery concept, whether that is something as subtle as showing it on the character screen or allowing you to name it, or the aforementioned idea to have it hang out with your character while out of combat.
I’m not the kind of person who expects realism in video games, especially fantasy-oriented ones, but I do think it’s important that if you’re going to play a Falconer, you should feel like a falconer and not just like a rogue with some bird-themed skills.
I know this is a trivial “flavour” suggestion and not something that would be high priority as it doesn’t impact gameplay, but I still think it’s important for strengthening the class fantasy and player experience to make the subclass really feel special and distinct.