Teams, SharePoint, Viva Engage - which to use for dept comms?

Teams should do just fine, unless you have some special requirements. Create a new team with all the users (you might be able to use a dynamic membership one), configure a channel or two for generic announcements that can only be published by specific people (i.e. enable moderation), and some that are "free" for all to share praise/recognitions/etc. As each team comes with its own SharePoint site, you can directly leverage this as a store for any documents you might want to share with the department, add them as tabs when needed, etc. Use the built-in tags (@channel, @team) to ensure people get notified.

It should also be straightforward to integrate with any HR system you might be using and you can take advantage of the many first- and third-party apps, bots and so on. For example, if you HR system already has a recognition functionality, it can feed data into a specific channel. Same for any sales data, or pretty much any tool out there - the vast majority nowadays have some sort of integration with Teams.

Remember that Teams also come with an email address, which you can leverage to ensure people that don't live in Teams also receive the important stuff. Though you might have to work with your IT folks to ensure all members can receive such email directly in their Inbox ("subscribers"). Channels can also have an email address (separate from the Team one), but you have less control over it.