Solved. (See my answer.)
I have a couple of startup apps using the desktop bridge. In the past they used to work fine. Now, probably after some Windows update, after a reboot they don't start when I first log on, and don't even appear in the startup tab in Task Manager. After I log off and on again, they immediately start, and also appear in the task manager.
More Info
They all use desktop:Extension Category="windows.startupTask"
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And in sign-in options I have "use my sign-in info to automatically..." turned off.
EDIT
The issue resolved itself after the last Windows update July 2019.
EDIT 2
Spoke too soon. The problem is back. And it doesn't (always?) resolve itself after logging off and on. And it seems like after a couple of minutes (much more than the 10 seconds of startup delay) they do (sometimes?) appear in the startup list (but perhaps only after I start them manually?).