I have not toured on a folding bike, but have seen a few others that have.

I did an Adventure Cycling (ACA) trip over a decade ago. The guide, his wife, and one participant rode Bike Fridays. The guide and his wife each used the Bike Friday suitcase as a trailer and each also had a rear rack. For airline travel, the bike went into the trailer which was a suitcase. I do not recall if the guide had panniers. The one participant had a rear rack with panniers, no trailer and no front panniers.

Photo of the guide's wife below:



One of the Bike Friday bikes with a trailer is on the left in this photo.



A lot of people have posted their trip documentation on this website, some used folding bikes:
https://www.crazyguyonabike.com/

There are a few other websites where people have posted their trip writeups, but I am not sure where. Others on this forum could list them.

When I think of bike touring on a folding bike, I think of Bike Friday bikes. There are other brands too, but the ones I have seen or read about were Bike Fridays with 20 inch wheels. They make a few models that have been used widely for touring. My folding bike is an Airnimal Joey with 24 inch wheels, I have not toured with it.

Keep in mind that folding bikes are a compromise. I suspect some will disagree, but my opinion is that some folding bikes are designed for portability at the expense of rideabiliy. And others are made to emphasize the ride, less focus on portability. My Airnimal is in the second category, it rides very well but is large when only the first fold is used and it takes a lot of disassembly to fit it into an airline sized case that meets the 62 inch criteria. But it would easily meet the Amtrak criteria for a folding bike as a carry on with minimal effort to fold to the Amtrak size.

I think first you should decide if you plan to travel by airline, airline size criteria for folding bikes is quite different than Amtrak. If you plan to only tour on Amtrak, you could have a bigger folding bike.

If you think you would only rarely need to fold a bike, there is the option of a coupled bike instead. These are full size bikes, but the frame can be split to allow it to be packed into a smaller case. Most common are S&S coupled bikes, many brands have built bikes with these couplers. Another option is Ritchey Breakaway bikes, those couplers are specific to that brand and model of bikes. There is another company out there that is selling couplers, I think it is a tandem bike company, but I do not recall whom.

Bike photo below is my heavy touring bike, it has S&S couplers on the top tube and downtube, so I can split the frame to pack into a smaller case. But packing and later reassembling a coupled bike is a chore that is measured in hours, not minutes.



If your plan is to rent an apartment for a month or two, then go to a different city and repeat, I would rent a car to travel to the next city and skip Amtrak. And if you did that, you could ship a full size bike by Bikeflights.com or Shipbikes.com if you were renting small cars.

I do not recall what vehicle we rented, but two of us drove a rental with our touring gear and two bikes in the back to where we started our tour. I think it was a minivan, below.



There is the right kind of bike out there for virtually anything you want to do, but you really need to figure out what kind of travel you want to do.

You describe renting housing, but you do not mention if plan to sleep in motels or camp. You really need to figure out more detail on what you want to do. When you say you want to have a full suitcase full of clothing, that is not a normal way to tour on a bike.

You certainly could use front panniers, rear panniers, both, etc., on a folding bike. But how much gear you want to carry will vary a lot based on where you plan to sleep that night.