I did several week+ camping/touring trips on bikes a number of years ago. I'm 62 now and looking at doing a few more now that I'm retired.
The camping gear doesn't need to be as expensive as outlined above, in my opinion, although you getter better gear, the more you're willing to invest. A good 3man popup tent can be had for under $100 and a cheap sleeping bag for $25 and double thick air mattress for $25. Three changes of outer clothes and maybe double that of underwear. Plus layered jacket for warmth. Plus a good tool kit with tire plug. flashight. It will easily fit in a backpack (army surplus alice for $50 or similar) or the topbag and the 2 saddlebags. A sleeping bag makes a great backrest, by the way.
There will be plenty of laundromats along the 2 lane roads and in small towns, and even in some state parks. Parks with covered picnic pavilions were my favorite spot to stay, get there at dark, and leave at sunup. No need to pitch a tent that way. Parks often have free shower facilities as well as some truck stops along major highways. If there is an extended spell of bad weather, or a couple days of sleeping out are getting old, then get a campground or go to a motel and soft bed to sleep in. If you see locals with cars parked at a bridge or lake edge, that may be a good spot to go swimming...
Food can be purchased at a grocery store for 1/2 or less than at a restaurant. Grab a couple cans of fruit juice and a hoagie sandwich and some beenie weenies and a box of donuts. Eat 1 good meal a day in a restaurant.