The answer turns out that all of the worlds we've been creating for years have been stored under "Application" rather than "External". and this setting stores them in a protected area of the file system which cannot normally be accessed either by USB or even the built-in file browser.
There are apparently three methods of accessing this area. 1) gain root access to the phone. Most people are scared to try this step. 2) For each world, upload it to Realms (using the 30 day free trial) and then download it to external. There are a couple of tricky parts to make sure this goes properly. 3) Some boffins created a tool called "Worlds Explorer" which takes advantage of an android backup utility to pull the data out of the phone and then extract the worlds. This seems the most painless but requires java and there's a whole lot of linked together applications that are needed to make it work.
The links:
The first thread that I found with the clue as to what the issue was. The answers are not great, including misleading once which advise starting to save to "External" (doesn't actually recover previous worlds stored in Applications, just makes sure your new worlds are in the external location) and a terrible write-up of the Realms trick. https://www.trueachievements.com/forum/viewthread.aspx?tid=989031
Another forum thread with a groping understanding of the problem, but then the creator of WorldsExplorer posted a link to his app: https://gaming.stackexchange.com/questions/311137/where-do-minecraft-pe-can-save-worlds-other-than-sdcard-games-com-mojang-minecra
A reddit thread that explains the problem succinctly but with no helpful answers: https://www.reddit.com/r/MCPE/comments/677n3a/i_cant_find_my_world_folder_on_mcpe_android/
Another reddit thread that explains the issue well. This thread contained a much clearer description of the Realms trick. https://www.reddit.com/r/MCPE/comments/7azwvd/so_is_it_confirmed_that_minecraft_worlds_saved_to/dped2qa/
This angel from heaven posted a YouTube video that simply and unambiguously walks you through how to do the Realms trick. https://www.youtube.com/watch?v=fdFIXZ2rfJs
Here is a forum thread that has reports from people who have used both the Realms trick and WorldsExplorer: https://feedback.minecraft.net/hc/en-us/community/posts/360009322871-Moving-Resources-from-Application-to-External-Storage-bedrock-mobile-originally-but-any-
Here is the link to WorldsExplorer (it's apparently actually called World Exporter): https://tikolu.net/worldExporter/
