I experience a similar issue on my Windows 10 device: during auto-saves, the game still runs, however my mouse input stops working, and GUIs will not open until the save is complete. I do not experience any of the other signs that you mentioned.
Thanks! Can you check if it still happens when updating it from 1.19.73 to 1.19.80?
Reply to GoldenHelmet on possible cause; so you mean that the addition of new boats will cause the problem? Also, is the damage done when you update, or when you open the world?