I LOL watching House Hunters/House Hunters International, all the people insisting on an "extra bedroom for guests", often for enormously more money, when they could simply put some of that money aside every month, put up guests at a hotel with it, & Everybody would be far happier!

Rent a small RV, (towable, so you can still have your car?) stay in their driveway...tell them you are thinking about buying one ......

All very good suggestions. I don't want to damage the friendship. They know me very well, so I suspect the truth will set me free! I'll incorporate those suggestions into my reply. Thank you.

I agree. As you already know them well, they no doubt know (or suspect) your inclination for privacy, so it may not be a complicated conversation, maybe even as short as "I would be more comfortable staying in a hotel."

Many people offer their homes to assure their visitors that it won't be a costly visit, so it's sweet of them to offer you the choice.

I always stay at a hotel and if pressed explain that I have medical issues that require privacy.
That usually does it.

The truth will set you free. Tell them exactly why you would prefer a hotel. You are an introvert. You have difficulty being with others for extended time periods. You like them so much and would LOVE to visit, but you need accommodations that allow you extended solitary time.

Thank them for the kind invitation and tell them you’d love to accept it, but only on the condition that you stay in a hotel. Say it’s a policy you have because you’ve had experience of staying with friends putting a strain on a friendship in the past, and you wouldn’t like to risk it happening again.