Why would it "confuse the heck" out of you? Most musicians study a variety of instruments. In particular singers benefit form accompaniment and piano is one of the best ways to do this. It's sort of an all purpose instrument in this way. Musicians will also try out arrangements on piano and compose on the piano, even if it's not their main instrument.
In the standard music curriculum (at least in the US) students are required (or at least strongly urged) to take "piano lab" regardless of their main instrument. They will also take singing lessons. Not with the intent of becoming a singer but to awaken the connection between the voice, ear, and other parts of the body. To develop a deep sense of ear-hand coordination. And to be able to hear music while you sight read. Learning to sing is NOT mandatory for developing this skill but rapidly accelerates it in my experience.
Learning to vocalize melodies is a standard part of learning any instrument in my experience and every private teacher I have ever had (guitar, classical bass, violin, horn, etc) has introduced sight singing into the lessons. In fact I recall that my bass teacher would have me sight sing bass concertos (one passage at a time) before attempting to work out the fingering and play it on the bass. It is often said that "if you can sing something you can play it". I'm not sure I believe this bit of "wisdom" as I don't see an objective connection between singing and say having finger dexterity. But one thing is clear, if you don't have a clue what you are trying to play you won't know if you are playing it correctly and sight reading has it's flaws as well.
Ultimately singing simply connects your inner ear to your body and that is helpful. That doesn't mean you need professional vocal lessons to get better at an instrument and certainly you cannot sing multiple voices at once, so singing piano and guitar music will not be entirely possible. Many beginners go through a period where they look at music and say to themselves "I wonder what this will sound like", whereas after years of training you can look at music and literally hear it in your head. If what you hear when you see sheet music is connected in your brain to a hand movement or other physical action then you are actually practicing just by reading without an instrument.
Do you need to literally sing to develop this connection? I do not think so. I can say from personal experience that I can do this with guitar music even if I don't vocalize. However, I might be wrong since I was trained to do this at age 4 by my violin teacher. So perhaps I've been "programmed" and don't know any other reality.
As a professional musician you will not always find work playing your favorite music on your instrument of choice. Being able to sing and find your way around the piano are great skill to have on a resume. I cannot count how many friends and colleagues earn $$ on a daily basis with their piano and voice skills (even if they're mediocre). Almost every audition I've been on for a guitar gig preferred or required the ability to sing back up.