Great thread and question Ivan, certainly a topic I have thought often about!
@hoshin1600 said it very well in his post, and my thoughts are along similar lines.
Yeah I don't know if emotion is the right term I would personally use, but feeling or energy, definitely. Each kata/form has a different feel, energy or principle that it's trying to communicate to you. And no, I don't mean in a new agey "it speaks to you" sorta way, but I sort of do
.
I've always seen forms as being much more than just surface level, and I include bunkai/application in that; as important as that is, there's a heap more under the surface to explore and connect with. Eg, the kata Seiunchin while meaning to grab and pull in battle and to be very rooted and grounded while doing so, it sort of commands that feeling of sinking low, being grounded, and mentally to really connect with that sense and feeling of "I am not moving, no matter what." Conjures up an elephant and the pure strength and heaviness.
When you practice forms with these sort of things in mind, it really transforms them and reveals some incredible stuff in them. Some might say it's just simply using sports psychology, and yeah for sure that's true, I guess I can see how it's more on an energetic level too how to tap into those different states of mind and particular energy, and how that not only expresses within the framework of the body but how it mentally/spiritually is instilled.
It seems as though the physical movements themselves can lend the concept as to what you should connect with mentally eg. Strong and grounded movements -> strong and grounded/immovable mind.
I know forms competition isn't everyone's cup of tea, and I agree with most the comments about it here. It's only happened a few times, but I remember watching the forms at a tournament, this one person performed and I was in tears... you could tell she just "got" it, and it was far different to all the other competitors, even performing the same form. It was like every element was in perfect union and harmony, body, mind, technique, spirit, understanding of the principles, concordant emotion/feeling on full display, freedom and self-expression... and it just knocked me out. I learned so much from watching that.
But yeah I don't mean the overly exaggerated showing of emotion, that's purely performance and you can usually tell if someone is just putting it on or genuinely expressing it. Ultimately forms should be an expression of yourself as well, so the way you express certain ideals, feelings etc will be unique to you as well. I'm also not a fan at all of the cookie cutter model that all forms should look exactly the same.
Coincidentally I actually just bought a book recently called "Karate: Beneath The Surface: Emotional Content of Kata", talks all about this (primarily Goju ryu kata, but still applicable for other styles).
And also specific techniques can also elicit these feeling connections too. But kata specifically communicate and instil in you a type of body intelligence, and delving into that is really quite fascinating!
Ah and I posted a thread a little while back on alternate exploration of kata involving what they bring up in you etc... I'll scout out and find it if it's of any use...
But as a note, these are all just my own thoughts on forms, and by no means set in stone nor should anyone feel they need to practice or see them in this way.