What is changing the default keyboard layout from "U.S." to symbols after hitting + in 10.15.7 on a Mid 2012 MacBook Pro? The event:
After updating to 10.15.7 on a Mid 2012 MacBook Pro and hitting first time the + key - &quot;é&quot;, the keyboard layout changed to symbols (instead of asdfg I get åß∂ƒ©).  I have only the &quot;U.S.&quot; keyboard layout installed.  A few years ago I had the Greek because it was easier to type greek letters, but removed it about 4 years ago.
Symptoms:

Of course I am unable to log in. /Sometimes I can, but I was unable to determine what sequence of trials /+, , , , +, +++, etc.../ sets it back to &quot;U.S&quot;.

The &quot;About This Mac&quot; menu item under the Apple menu disappear.  A new menu item &quot;System Information&quot; appears.

When I am in an Application - let's say Safari -, the &quot;Quit Safari&quot; menu item changes to &quot;Quit Safari but keep the Windows&quot;


Remedies tried:

All the key combinations and more listed above.  Did not work
Chat with Apple Support twice.  They had no clue but recommended to reformat and reinstall.
Reformated all volumes that Apple allows to reformat and reinstalled from the Base Mac OS. Did not work.
Reformated again and installed 10.14.6.  Did not work.  After the first hit of + or +, the keyboard layout changed to symbols.  Upgraded it to 10.15.7, hoping it will wipe the Base Mac OS clean and updates the EPROM... Did not work
Tried to boot from an USB drive that is bootable and contains 10.15.7 but after the Installer rebooted the machine the install did not continued from the USB drive, but rather of the Base Mac OS stored on the internal drive. So, ultimately did not work.

Any good suggestion that will work to keep the &quot;U.S&quot; keyboard layout?
It sounds like your machine thinks the Option key is always depressed.  Make sure that you do not have Sticky Keys in Accessibility Preferences turned on.  Try an external keyboard (doesn't have to be from Apple) and see if the problem persists or not.