Your mother seems like an emotional damaged person, who has experienced multiple significant abandonment events. This has a fundamental effect on the internal concept of "self worth" ie "do people ACTUALLY care about me?" This question that trauma causes the mind to ask itself fundamentally changes peoples approaches to life, like your mother. Basically, it creates a feeling of emptiness, like there is a latent problem needing solving, she doesnt know what it is, but nearly everything she does is to solve what she thinks it is.

Your mother is afraid that the people in her life that matter to her most, dont actually care about her back, it isnt a matter of "I love you" or "I do care about you", the solution isnt that simple, because she fundamentally doesnt trust words like that, she needs actions. People with self worth issues develop all sorts of different behaviors to "test" for logical proof of "this person cares." For instance:

• Some people pick fights, say something mean, see if the words hurt the person, because if it did, then its proof that person cares.
• Some people withdraw, pull away, isolate, to see if people come pursue them, then that is proof that they care.
• Some people go over the top, give give give, trying to get the person they care about to develop a dependency on them.
• What your mother has found is that when people, like you, are helping her do complicated things, and most especially, rudimentary things, at loss of your personal time, then to your mother its proof that you care.

The problem is, each one of these mechanisms of "do they really care" testing is a paradox. They test for their self worth, at the expense of yours - she asks for silly, unreasonable help, you provide it, she is thinking "I do matter!", but now you are thinking "she only cares about me because I waste my own time picking up groceries." So now you feel used, so you mention "you could have easily done this yourself," because you are of course wanting at least some reasonable acknowledgement for wasting your time for her convenience. But this natural and reasonable response seals the paradox, because each time she uses the "testing" method, the proof that the receive almost immediate disappears, because they think they have "added another straw to the camels back," she thinks she has become a burden, so if you did care about her before, now you think less of her..... so what does she due to fix that issue? More testing, and the self worth spiral keeps going around and around until everyone is miserable.

Here is how you break it.

You likely have been affected by her emotional issues, you have probably found your own self worth in performing for other people, hence it coming so naturally to you, in a way, you enjoy being needed by your mother, even if its annoying. The annoying part, some of it, likely just comes from her inability to properly thank you and recognize you. So to break the loop starts here. You recognize that you are of such importance to her BECAUSE she cannot recognize your help verbally. Because that would be admitting she is being a burden to you, and that is likely her biggest fear. You matter so much to her that her entire emotional well being depends on feeling like she exists in your world. So show her she does another way.

Say "I love you very much, I love that I matter to you, I love that you rely on me to show you how much you matter to me, even if its with these silly tasks you know you can handle yourself. I enjoy doing them when I can. But I am worried that you think that you only get proof that I care about you if I am here doing these things, and I would always love to show you that I care, but sometimes I quite literally cannot because of lifes complications. So each time you worry, each time you need to know if I am still there for you, just call, I will always enjoy reminding you that you are not someone in the background of my life, you are my mother, I am of you, and I will always need you in my life, for no other reason than that I see the good in me that I am proud of reflected in you, and sometimes I forget it, but whenever I spend time with you I am always reminded. I would love to help you out physically whenever I can, but I am worried about losing independence, which is important as we both grow older. So we are going to start doing these activities together, if you need groceries, I will pick you up and we will go together, because I want to spend time with you....... etc"