OP if it makes you feel better, some educational philosophies like Waldorf highly value children seeing their parents perform physical tasks such as cooking, cleaning, crafting, farming, gardening, etc. The crafting is called "handwork." They believe that children learn best through imitation and that by seeing adults around them engaged in mindful physical activity, they learn to develop their own powers of attention. Basically, they learn to play by watching us work. When I heard that, I was like, oh good, I'm not neglecting my child if I tell her "I will come help you when I finish this row".... lol. Of course I drop what I am doing if she is in real distress, but we practice a lot of patience stretching too.
Anyhow, my DD is also around 2.5 and for some time now we've been learning to work side by side. I want to point out that during her first 18 months I ended up quitting my job as a freelance copywriter because she would scream whenever I was on my email or phone. So she's not a super baby, she's a normal kid who hates to see my attention be on some stupid box.
Around the time she was maybe 20 months, I began crafting with her instead of while she was sleeping. At first I sat down with my knitting and gave her her own needles and yarn. I sang a made up knitting song (it's easy: "I like knitting, I like knitting," to any tune you like) and she sang it with me. I let her handle my projects and many things were frogged, many needles were lost, and many yarns were tangled. Once I was satisfied she'd had some chance to explore what I was doing, I began to insist that she use her needles and I would use mine. Now I just take away my projects if they end up in her hands. LOL. In the beginning it was just five or ten minutes. Now probably a half hour at a time. Sometimes she "knits" next to me with pretend yarn, sometimes she talks to herself, sometimes I tell her a story. Sometimes she rummages in the scraps bin and cuts yarn and fabric into thousands of very messy, mangled, and tiny pieces.
Anyhow, while I was knitting this afternoon, she bounced on the couch, then found a little needle felted ball on the floor, grabbed some yarn, and asked me for her scissors and a felting needle. I figured either she'd hurt herself and give the needle back or she wouldn't hurt herself. Either way, she wasn't backing down about the needle. So I gave it to her. She sat down, cut the yarn, and began to felt it to the ball. "I'm making a baby chicky," she told me. "Probably it's a cat." She worked steadily. I heard "Ow" once, but she worked until she was ready for me to make a few finishing touches to it. "You help me, mama." Then we put the needle away. Later she was playing with her new baby chicky.
I really believe that when we take our work seriously it gives them the ability to take their work seriously too.