I don’t like carrying a separate garment bag. I’m looking for a single piece of luggage that will fold a suit like a garment bag but also let me pack everything else in the same suitcase and check it without worrying about the suit getting wrinkled. Any pointers? Maybe I just don’t know what keywords to search for.
I’ve also seen this wooden and metal device with a hanger hook on one end that you lay your suit in and it has a hinge so your suit can be folded and inserted into your luggage. Maybe that’s what I need, but I don’t know what it’s called. I’d really appreciate a link to where I can buy one.

There are a thousand and one on-line luggage sellers. I have personally used and. Both were excellent. ebags calls what you are looking for a “garment sleeve”.