Have a timer/events continue in background while user is typing an input?

The simple use of terminal with the staple input and print functions will not work for what you want.

For once, when performing an input your program thread simply pauses for "reading" the stding file, and will only unpause when the user hits . Keeping an internal count ongoing in another thread is somewhat trivial to do - but displaying any values in another portion of the terminal is not that easy.

stdin and stdout - the files presented by the O.S. for all communication with the terminal, ordinarily will just allow for all output (and input interaction) to show up in new lines at the bootm of the terminal, scrolling the content up.

ANSI Escape codes exist as an upper-layer protocol which allows for things like colored output, cursor positioning, text attributes, and such - but Python's input won't be aware of those.

The way out is to use a TUI (Text User Interface) framework, which will allow you to have widgets for terminal control,just like GUI Widgets for a "text entry" - they will take care of handling the ANSI sequences for you, and outputting your updated timer in a region of the screen, while new keystrokes will update another region of the screen.

I suggest you go forward with textual - it is a modern framework that will allow you to use asynchronous programing to do a thing like having a timer being updated while waiting for user input on the same terminial screen.

Otherwise:

Congratulations for learning to program and Python - but your project had reached the limits of what is possible with print and input as put above: maybe instead of passing to a necessarily complex TUI (because non linear input/output interation will imply in complexity), you can upgrade yourself out of the terminal if you want - Python comes with tkinter built-in: a framework for windowed GUI applications, which will also be nice for your project, and could, maybe, be more fun to you than a TUI interface right now.