I can't offer current on the ground info for any of those locations, but I can offer some advice. I have camped in the town parks in many of those towns without issue. I have done similarly in other towns across the Great Plains and other areas of the west. I generally never had trouble finding an impromptu place in small towns. I typically didn't ask permission, but did sort of feel out the locals for whether I'd be run off (I never was). It looks like many of the towns you will pass through are on the TA. For places on the Trans America or other well established ACA routes the maps are a great guide and the addenda will be updated frequently as the season progresses. It might be worth buying the relevant ACA TA maps if you don't have them. Download the latest addenda before you start and again as you get closer to various sections.
I'd think that most of the places I stayed on the TA or the ST would not be very subject to closure since they were not really open to start with. Many were picnic areas or other little town parks. Restrooms or other facilities may be a bigger issue, but you will figure out a way to deal with the current situation as you go. For sure that is the easiest part of the country I have found to improvise free camping in little towns. I generally just pitched my tent in the town park. I'd ask the local cops if the town was big enough to have cops, but it almost never was. I'd usually buy something in the general store or whatever store there was and say something like, "I am riding coast to coast. Do you think anyone would bother me if I pitched my tent for the night in the town park over there?", Alternately, I might ask folks I ran into if they knew of where other cyclists might have camped when passing through. If really stuck, librarians, clergy, cops, and firemen are good people to ask about a place to camp. I have had librarians call around and find me a spot and the other three offer one that they had jurisdiction over or knew of.
I really doubt that Covid will have much impact on any of that. I have heard that it has had an impact on the ability to fill water bottles or to use restrooms many places. Some reported needing to buy bottled water frequently. I don't know how much it has impacted the frequency that you will be offered hospitality, but I'd guess there will be an impact. I imagine there will be some return toward normalcy as compared to last year, but it may be slight.
When do you plan to start? How well the addenda will be updated will depend on whether some of the TA coast to coast traffic has passed through there yet.