The appliqué is stitched in place with a very fine blanket stitch
Some of the yellow fabric has a colour-graded weave.
Looking at the back, you can see how coarse the background material is. Also, I was slightly surprised to find that all the stitching appears to have been done by machine.
I compared it with a tray cloth that I have because the yellow fabric used for the appliqué is so similar. The stitching on the tray cloth is definitely done by hand, and so much finer than the stitching on the doily, but they certainly seem to date from the same epoch.
I have been debating how to use the doily. Tempting as it is to stitch it to a background material and use it on a quilt or cushion, I think it would disintegrate too quickly. Perhaps it would be better incorporated into a plate stand. It might be time for a consultation with my husband about how best to make one.