Some rescue cats are that way, particularly if they were separated from the mother too early. My old glorious golden fuzzball "RJ" (now RB at age seventeen) was that way for at least a year. He stuck to me like glue.
My recommendation, aside from being thankful that you're so loved! is to get several very nice cat toys for your cat to own and play with. Of course you know that already. It does help, maybe something springy and safe for individual play without the human to "operate" it. ha ha
What I also found out was that if I got several small cushiony pillows for RJ to lie upon, while being close to me, either when I was reading or working on the computer, or in bed. Having their own cushion lets the cat add its own scent to the pillow and it feels more homey. If the cat likes to lie on the pillow and also be close to you, you can sloooowly move the pillow a bit farther away each few days, creating a small separation space.
As for the cat crying, this is normal and there's really nothing you can do, except when you come home, pick the cat up and love the animal closely.
Our Bobby cat cries when my girlfriend is out of the house more than a couple hours, even when I'm home (he likes me but LOVES her) and even with our new adoptee Callie cat, Bobby still cries.
Incidentally, does your new cat have good hearing or is it deaf? Some mixed-eye white cats are deaf. If so, that's okay, but it gives you a focus for buying cat toys, skipping on the squeaky type and just getting the fuzzy and fun type.
And of course, you KNOW that you're lucky to be so loved, right? And yes, we all know that it's frustrating to have a sticky-cat shadow, but hey.... go for it.