Ungoogled Chromium is Chromium with all google domains and google-specific code removed. It keeps the nice things about Chrome/Chromium like the dev tools and is compatible with Chrome extentions, though you do have to download and install them manually. Unlike Chrome, it is also 100% open source.

How timely are updates? Would be my main concern here.

I was under the impression that Chromium had some Google integrations but was pretty harmless from a privacy standpoint unless you sign in to Google. Is that wrong? Do I need to use Ungoogled Chromium instead?

It's a fork of Chromium, the core layer of Chrome, with Google integrations removed (and other privacy-conscious feature removals/additions).

https://github.com/Eloston/ungoogled-chromium

How is this different than Brave?

Brave is based on cryptocurrencies and selling eyeballs, with users getting a share. It's a for-profit startup.