I recognize in you what I see in many of my own relatives. Offering highly precise and specific solutions when I don't even yet agree there's a problem to be solved. One example: years ago a boyfriend suggested that I transfer from my university to a different one closer to him. He gave no explanation or logic, just started with that, and as I kept asking why he was bringing it up he finally blurted out "I'm asking you to marry me!" The good news is, I did, and we're still married nearly 40 years later. (But I didn't transfer to a different university.)
So how about backing up 6 or 8 steps in that conversation with the probably-can't-shop-any-more person. You've decided they can't shop. You have two solutions: let them order stuff online, or you go do it. They are rejecting both for one stated reason (no-one can do it as well as I can) and probably also one unstated one (I don't want to lose my powers.) As someone who faced a frighteningly fast decline last year, unable to do many everyday things, I know how that feels and how strongly I clung to the few things I still could do. (I'm better now, if that's relevant.)
So, you start much earlier in the logic chain.
I bet [recent injury] is making it harder to look after yourself, isn't it? I mean I can see you're cooking and cleaning just like before, but I'm thinking of things like making the trek to the shop, that must take a lot out of you.
If you get agreement that yes, some things are more difficult than they used to be, you're making progress. If they aren't more difficult, then hey, just because you know a way to make things easier doesn't mean people have to accept it. After all, we all need to fill our days somehow. But let's assume your relative concedes there may be some small issue in some aspect of the current shopping situation what with [injury] and all. Now, you want to offer help, but not solutions.
Is there anything I can do to lighten your load?
They may have something in mind. If they don't, you can make suggestions. My uncle used to get all the heavy generic groceries for his mother: large cans or bottle or jars, carton of milk, case of old-people-protein-drink, and so on. These are things you can buy from a list, you're told what brand and size to get, you get it. Then she got bread, veg, and other things where her personal judgment was relevant and important. The few items she was going for fit in the basket of her mobility scooter so it was a much easier shop. While I was ill, people drove me to stores and carried things for me, but I did all the actual shopping. You could also suggest the online for the non perishable heavy stuff and that would make the trip to the actual shop faster and easier.
All these should be phrased as questions. "Would it be any help if" or "I wonder if I could" or the like. They need to be vague, too.
I wonder if it would help for me to get some of the super heavy cans and bottles stuff for you, the stuff that keeps, maybe on my way here next time? I understand it wouldn't deal with everything, but then again you're more than capable of going shopping, it's just that the heavy stuff can be awkward for you at the moment. I really would love to help make things easier for you.
Why should you be vague? They need to be the ones to come up with the precise solution to their problem. They don't want you diagnosing a problem, and solving it, and telling them that it will be this way now. They want to be in charge, for their opinion to matter - about what veg to choose as well as how the shopping gets done.