doom-emacs VS company-mode

You can take a look at the default init.el file for Doom emacs here, as you can see, there is a :lang section where you can uncomment support for commonly used languages. Although you generally don't change the init.el file too much, usually, it is there to load your actual config files. If your language is not supported out of the box, there are ways to add packages (a.k.a. "plug-ins") in packages.el. And you can add customizations in config.el.

I'm curious to know what `company` does differently here than `corfu`. As a longtime user I couldn't be happier.

https://company-mode.github.io/

they wrote the first word and auto-completed the rest

For me, it's http://company-mode.github.io and maybe a touch of all-the-icons..

I'm not sure if I did anything special to enable it, but I'm pretty sure company-mode does this

When I started using Emacs I was following the setup outlined by System Crafters, which I still think is a really good introduction. But, over the last few months I've started to replace packages with more "minimalist" or "stripped down" packages. I've switched from Ivy and Counsel to Vertico and Consult, and recently I switched from company to corfu for auto-completion.

As for the Emacs configuration, you should only need a few lines of code, in order to get them up and running, if you are planning to keep your setup as close to vanilla as possible. If you are interested, you could additionally install a completion framework like company-mode to help you out.

As for auto-completion, there's a few different variants that people use. Auto-complete being one of them, but an alternative you might want to try is http://company-mode.github.io/

For the company-mode see Frontends.

Company is a classic, though corfu and cape, also by Daniel Mendler is really excellent.