Are there any effective ways to deal with shadowing behavior?

To answer your question about groceries, sometimes I order online from Walmart and just drive over and pick them up. As for shopping in the store, it's a matter of profound wonder, as Abe Lincoln used to tactfully say when talking about his marriage.
She wants to help, but has no idea what we need, and puts things in the cart that we have plenty of at home. If there's not much cost involved, I just go ahead and buy it, otherwise I discreetly take things from the cart and put them on any shelf before we check out . She never once has asked what happened to ____? I stopped trying to surprise with anniversary cards, flowers and gifts, I just let her watch me pick them out and check them out.

You know what's really ironic? She has always said she hates surprises. Now everything is a surprise, even if I told her something 5 seconds ago. She will say, "Oh!! Why didn't you tell me that?" And sometimes I just say, "Sorry, I must have forgot!" Other times I just don't answer.

I think of my husband as wandering through a foreign land with no navigation tools. I am his guide.

I love this quote - I think it's Teepa Snow:
"You may only be one person in the world, but to one person, you may be the world."

Yes, which does explain the shadowing. An understandable fear of losing her world is present every waking moment.

It must be so scary for her.

I remember my absolute panic as a child when I was separated from my mother in a department store and couldn't find her.

Same thing. Horrible fear that you couldn't get back what you so desperately needed to survive.

This is such a great question.
I’d really like to read more responses to this.
I get up early so I have an hour to myself. If my husband hears me (veerrryy quietly) making a cup of coffee, he will be directly by my side. I have tripped over him, and spilled things, because he is always ‘right there’. I have asked him to please not hover and to keep one arm length between us for safety.
If we visit others, when he answers a question by a friend, he will look right at me as he answers.
He needs my constant attention.
At this point, I can ask him to do small tasks around the house and that gives me some reprieve, unless he starts asking me for input on every step of the task. I try to make a deal with him, that we will do something he would enjoy, then I get some time to do the finances, appointment making, etc.
Right now I am writing this in the bathroom with the door closed - so my ideas only work for so long. 😄

I have a similar situation. My husband doesn't shadow me but wants me next to him at all times. He suffers from chronic pain so mobility is compromised. If I walk away, even a few feet from living room to kitchen, he calls out to me. I'm only a few feet away (small condo) and we can see/hear each other but he wants me to walk over to him to talk to me. Often, he's forgotten why he called or he repeats some nonsensical thought.

He doesn't want visits from friends or family, just me. The occasional days where he sleeps all day are what saves my sanity. Not sure how long this is manageable. 😞