Onion "sets" are small bulbs and onion "seedlings" are the small immature plants started from seed.

A few years ago I planted "sets" and had a similar experience with bolting. Even though they are commonly sold in our garden centers, I am not sure if sets planted in spring can be successful in our area. At the end of last summer (August) I started Keepsake onions from seed and then planted them in the garden as seedlings in October and they overwintered and produced beautiful onions which I harvested a few weeks ago. You might want to try this.

I don't think that the weather (this year) is a factor of your crop bolting. You can use these onions, but they will not keep. I would pull them all and use as many as you can and chop and freeze the rest. This works quite well. Last year I had them same problem with Spring planted seedlings because of the wet spring and that I may have planted them too deep

If you truly have "sets" I would wait until Fall and try to overwinter them...but I would ask on the Allum forum as those folks might have more accurate answers

The ones that flowered, should be used soon and are not keepers. They will rot of kept longer.

I have planted in the past both sets(over wintered) and seedlings in the spring. The sets tend to bolt more than the seedlings. With the sets, you have to use very small ones. Bigger once have a higher chance of bolting.

Not every onion, be it seeds, seedlings or sets, is a ONE SIZE FIT THEM ALL. Onions are daylight/ latitude sensitive. It is whole new ball game growing onions successfully. Of course, everybody can plant them. So, I just plant onions for greens(scallions) and buy the bulbs from stores.