That's not what I thought of when saw timothy hay. That is a rabbit food with a lot of stuff in it in addition to timothy. I did not see anything in the mix that they specifically need, but I did not see anything that will hurt them. The marigold petals could help make their yolks darker. On that ground they are getting plenty of grit so they can grind it up in their gizzard.
As a treat, it should be a fairly minor part of their diet. You do not want to upset the balance of their nutrients.
As you saw, they will slurp the long stems down. There is a risk in that if they get too many at a time. If those long stems get twisted up in their crop they can form a wad that cannot pass on down through their digestive tract. That is called an impacted crop. Any that gets to the gizzard will get ground up but that doesn't help the crop.
This is why some of us recommend that you run grass clippings through the lawn mower an extra time, to chop the grass stems into shorter pieces. If they were foraging on that timothy where it was growing they'd break it off into smaller pieces, but it is not rooted to the ground so they eat the entire length. Rabbits will chew it up so the length is not a problem to them. The other stuff is not a problem at all, just the long stems.
So severely limit how many of those long stems they get or cut them up into 2" pieces or shorter.
Do not panic about what they have eaten. They should be fine. But if their crop has not shrink to empty by tomorrow morning and it smells sour you might want to investigate impacted crop. This is something that can happen, not something that happens each and every time.
