IntelliJ GIT ui/ux is so completely frictionless it's magical at times. The only downside is that it makes incredibly complex operations trivial that I never learned git from the cli beyond the very basics.
Not the biggest deal since neither of those commands require interacting with the output which makes them equally easy to run from the terminal, but it's strange that they're not available in an immediately obvious place.
In the lower right, there's the vcs "where you're at" that shows the current branch. From there you can see the status of your branch compared to others (if you need to fetch them), or you can update branches (even those you're not currently on) along with branch specific operations including push. You can access the same in the git panel with right clicking on branches in the log.
At any time, you can double tap shift to bring up the "search everything" window. Within that, if you type "git push", it will display that action along with the menu that action is in and any key shortcuts that are bound to it.
Also, glance under the "Help" menu - there's a productivity guide. That shows you a whole bunch of features (and how often they're used) and how to use them.
Maybe you disabled the git toolbar in the menu?