What's the Jewish idea of how people will interact with each other after Resurrection? Since there will be bodies, will the interaction be as it is now, or since people will be so spiritual, the interaction will be more on the level of the soul?
This is a very interesting question.
To appreciate the answer of what it will be like in the ideal state of the future, it's necessary to consider what life was like in the precedent for it – namely in Eden before the downfall of Adam and Eve.
Mystical sources in Judaism describe this couple in the initial, ideal state of Mankind as "beings of light". They are portrayed as reaching from earth to heaven, and with the ability to "see" from one side of the world to the other.
Yet, they were also creations in the physical world comprised of the material, and with the limitations of this-worldliness. Accordingly, how are we to understand the previous teachings that depict a transcendental state of existence?
Before the sin, Mankind was on such an elevated spiritual plane that the material of the world paled in the brilliance of their pristine perception of G-d. Since their own souls were similarly intensely aglow, they did not relate to each other on the physical plane but rather interacted on the soul plane. What's more, the bright inner light of their souls actually "energized" their bodies so that they took on a quality of this light as well.
In this way, they were beings of light. This can be understood when we consider our perception of a burning light bulb. The body of the bulb is barely visible in the light of the energy emanating from within it. In fact, the bulb itself glows with that energy. So too, in the ideal state, the brilliance of the soul both conceals and transforms the body.
This can also be appreciated through another common life experience. Try to think of how your best friend looks. It usually takes time. Most people who have such very close friends paradoxically lose sight of what they look like. This is precisely because as such close friends, they interact on a much more internal plane and no longer see bodies, but each other.
When Adam and Eve transgressed, their inner light was greatly diminished such that their bodies became opaque and visible. This is what's meant in the Torah by G-d's en-clothing them in garments of skin – their heretofore spiritual bodies congealed to flesh. Furthermore, in this light, we can understand the revelation of their "nakedness". The concealment of their inner light blinded them to the soul, thus deflecting their vision outward, "opening" their eyes to the heretofore concealed physical aspect of the body, now exposed.
It is to this plane of interaction that they plummeted, and it is on this plane that people interact till this day.
But according to the Jewish idea of Resurrection, people who seek the light of spirituality in the current state of concealment will merit the reunion of both a purified and perfected soul and body, resurrected and restored to the state of Mankind before the downfall. In that realm and on that plane, people will interact with each other not as they appear now but rather as they really are.