Caught between local and Microsoft accounts

One of my Windows 10 systems is in a weird state in between local and Microsoft accounts.

1. There is no "Sign in with a Microsoft account instead" or "Sign in with a local account instead" option under Settings/Accounts/Your info. This page shows my local account name, which is just my first name, and my Microsoft account email address. (I upgraded just a few weeks ago from Windows 8.1 and never signed in with a Microsoft account as best I can recall.)

2. My other machine is working right. When I switch to my Microsoft account, it shows my full name and email address. When I switch to my local account, it shows my first name and "Local Account" instead of my email address. There is the complementary "Sign in instead" option in both cases. Note the differences here between this machine and the situation described for the other machine in (1). (I upgraded from Windows 7 a few months ago, and I know I switched to a Microsoft account early on before switching back to my local account.)

3. The old-style Control Panel "User Accounts" shows "Local Account" for (1).

4. The local and Microsoft account names and passwords are the same for both machines.

Any ideas?

5. I log onto both machines with the local account name, which is just my first name.

Clicking "Stop signing in to all Microsoft apps automatically" in Settings/Accounts/Your Info restored things to normal. I've been using a local account all along, and I must have enabled that option when I ran Solitaire or Minesweeper for the first time earlier this week. Now, "Sign in with a Microsoft account instead" has returned to Settings/Accounts/Your Info, and there is no option to sign into all Microsoft apps automatically. I guess that option is reserved to apps for the purpose of confusing the user.