Hoping that the "refreshed Github" has extra features - first tried entering those commands at the "Command palette" in the Github.com web interface:

Not working. Obviously not the right place.
Installed Github Desktop, "cloned" my repository locally, but again no place to enter commands, referred me to yet another tool to install: "Git"
Installed Git (which installs 100 other stuff like editor, SSH, etc.?)

1. git reset HEAD~4 - seems OK
2. git add . - seems OK
3. git commit - opened some kind of text editor (vim??) with some pre-filled comment, but I couldn't "save" it
4. opened GIT GUI - clicked "Commit" button, wrote comment, seems OK
5. git push --force (or GUI "Push" button and then "force ..." checkbox) - doesn't work. In the background appears "Git credentials manager" console - if I click on it "Required command not provided" or something like that flashes in red quickly...
6. Force-closing this background window, AFTER Windows terminates it makes another window to appear: "OpenSSH Login". Entering credentials there doesn't help.

Takeaways:

• it's something simple/obvious that I'm missing (like entering my credentials in yet another place, probably in Git somewhere?)
• Github web interface should provide "command prompt" equivalent supporting those git commands.

git commit - opened some kind of text editor (vim??) with some pre-filled comment, but I couldn't "save" it

Yeah, that's probably vim or vi by default. Type :wq to save and quit. You can also just do git commit -m "My commit description" instead to skip the editor

git push --force (or GUI "Push" button and then "force ..." checkbox) - doesn't work. In the background appears "Git credentials manager" console - if I click on it "Required command not provided" or something like that flashes in red quickly...

Get the exact error message for that. I believe Git for Windows has a special GitHub credential manager that should just work when you type your GitHub username and password into it. On other operating systems, (like what I had to do on Linux) you have to make a "Personal Access Token" and use that as your git password: https://github.com/settings/tokens

I believe that's not needed on Windows but maybe worth a try if you want to bypass the credential manager.

If you want to hop on Discord I might be able to help you further.

@weirddan455 it seems the git-credential-manager.exe is being run by git.exe without any parameter. The text that flashes quickly seems quite similar to what I get when running it manually:

C:\Program Files\Git\mingw64\bin>git-credential-manager.exe
Required command was not provided.

git-credential-manager

Usage:
  git-credential-manager [options] [command]

Options:
  --version       Show version information
  -?, -h, --help  Show help and usage information

Commands:
  get          [Git] Return a stored credential
  store        [Git] Store a credential
  erase        [Git] Erase a stored credential
  configure    Configure Git Credential Manager as the Git credential helper
  unconfigure  Unconfigure Git Credential Manager as the Git credential helper
  diagnose     Run diagnostics and gather logs to diagnose problems with Git Credential Manager
  azure-repos  Commands for interacting with the Azure Repos host provider

Maybe I need to first "store" and/or "configure" the credentials manager...

For now, FeralChild64 managed it on his side, so that's OK.