With python, it's more about simplifying the entire process (a.k.a. making it pythonic). In my experience, it tends to be a wrapping mechanism around some binary or api so it's hard to pin point "an exact script everyone runs". Some are clean up scripts that clear out caches manually (until a fix can be pushed), others (like this one https://gitlab.com/sunset-crew/nextrelease) wrap git so you don't need to remember all the things associated with pushing a release and/or tag. Ansible, though it's made in python it's kinda it's own langauge, might be a good place to look if you want scripts that are generic enough for everyone to use.
I've written for teams and myself.
Both. Terminal, and some sort of automation. With Ansible, there's awx and semaphore. I think someone mentioned cronjobs, also systemd-timers. I think kubernetes has a cronjobs feature as well.
I usually have cron jobs set up on servers for simple things.
If I'm doing large scale web development, I tend to use containers, so I'll use a scheduling mechanism appropriate for whatever framework I'm using. For example, if I'm building a Django application, then I use Celery.
There's always the tradeoff of just using the tools you get for free in a Linux distro, but paying the price of handling multiple DSLs, versus installing, configuring, and managing a larger system with a more homogenous interface.
