Yes, plastic canvas projects like the one linked above work well at that age. The plastic is easy because it holds its shape and the squares are easy to identify.
I also second the latch hook rug idea. My just-turned-7 daughter is on her third rug.
Loom knitting is easy enough for a 6yo.
My oldest was able to handle knitting with needles at about 8yo, but not when she tried it the year before.
Cross stitch might be manageable for a 6yo, but I would start with the ones that are pre-printed on the fabric, not counted cross stitch.
As for the sewing machine, with lots of guidance and supervision my kids have been able to handle simple projects at 6. We made wizard capes, which just involved hemming the bottom, and then putting in a drawstring at the top. I think my kids were 9, 7 and 5 at the time. Right now my 7yo is interested in sewing squares together to make a quilt-style pillow case. (We need new covers for some of the throw pillows they use in the playroom, and we have a bunch of random scraps, and she has seen me quilt, so that’s the idea she came up with.)
