While learning vim/emacs and CLTs may not make you a better programmer, but they can absolutely make you better at understanding and using your tools effectively.
One simple thing I like to do at every job is setup an ansible playbook for the team I'm working on. What ansible allows is me to setup a tool to download all the relevant languages, binaries, create company specific repos for directories, establish a foundation of common CLTs, automatically install software, and fully setup all the paths. Now any person, old or future hires, can literally set up their machine in less than 10 minutes; an activity I see people usually give a full "week" to do.
This is just one example of being more productive with these tools. What's nice about vim are vim motions, they become extremely intuitive and all the supporting libraries, plugins, and other CLTs utilize these vim motions which makes productivity extremely nice.
If you want to see someone's workflow I'd checkout ThePrimeagen's video on his workflow:
I don't know why you are conflating these things with the editor one uses.
*Edit: Why the downvote? Tell me what I'm missing instead.
Most of these tools I tie in with vim hotkeys to shoot off various things. For example, I use telescope to jump between different git worktrees using vim motions or when using tmux I have vim motions mapped to maneuvering around panes (tmux cmd + hjkl) or going back to previous window (tmux cmd + o).
I'm not saying you can't learn to use these tools without vim/emacs but in my limited work experience those developers that use vscode for everything tend to be completely lost when the terminal takes the fullscreen.
I’ve been building corp infrastructure for a decade and I can tell you first hand how much of an impact fast, stable, updated environment can have on organizational productivity and overall output. I doubt devs are some how excluded from the pack.
The old proverb of shit in shit out also applies.
I've worked on teams where some members used IDEs and others used traditional text editors, and what differentiated their productivity was inevitably between their ears.
What the vim movements do is allow you to focus on your code without interruption. You can do everything without shifting your focus from the block of code you're currently editing. It's hard to describe until you've experienced it. I think it's just easier to get into and maintain a flow when the editor gets out of your way.
Our experiences differ with regards to the correlation. In my career I've seen a massive discrepancy between effectiveness of editor use and developer impact. Off the top of my head, save for one person (who used Sublime), every outstanding engineer I've worked with have either used vim or emacs.