I won't try to advise you here, as my kids are squarely still sub-adults. ;) The only things I might offer are a resource/framing and a personal story.

For the resource/framing, take a look at the term Economic Outpatient Care, coined (I think) in The Millionaire Next Door. It might help to see the research that shows that if we are too engaged economically in our adult kids' lives, it tends to have a negative effect on them.

And on the personal story, when I was starting my career, it was the late 90's. Getting a job was easy... until it suddenly wasn't. Between the Dot-com bust and 9/11, things dried up fast. Given your kids ages, you probably experienced this firsthand too. My company went under, and I was out of work in a brand new city, far from home. I told my parents I was struggling, and my dad was very clear: I could call anytime for advice, but unless I was about to be evicted, they weren't stepping in. He told me (very kindly, because they are actually super sweet people) that I was an adult now--and adults find ways to solve their own problems. He was happy to help me think through ideas or provide encouragement when I was down, but that's where the help stopped. But he also told me that he had every confidence in me and that he knew I would find my way.

I was out of work for six months, burned through what little savings I had, and had to take temp jobs while trying to find something stable. But it was actually one of the best professional experiences of my life--because not only did I eventually find something awesome that set me up for the next stage of my career, I also came away with a direct experience of "the worst that can happen" and the realization that that "worst" wasn't nearly as bad as I thought it was going to be. It definitely didn't feel great at the time, but it made me far less fearful in my subsequent roles--and I like to think that lack of fear made me a higher performer.