The short answer is yes.

If you're in a conversation about Shizuku, you should probably be downloading apps from the source. I've donated the equivalent of buying the app, but you don't have to pay anything to get the full features.

A lot of open source developers subsidize their users by charging on the Play Store while offering the complete app on F-Droid or other code repo (like GitHub).

giving file managers access to some directories that are normally not accessible to apps

That's something that might interest me, thanks!

Some features of the app claim to require shizuku, maybe the app itself is lying to me?

It's kinda like root-ish privileges. It facilitates doing things that you're not technically prohibited from accessing, but there simply is no interface for. It uses administrative console commands (administrative in the management sense, not like administrator=root sense) to execute changes that don't have any pathway built-in for the end-user.

Personally, nearly all my devices are rooted, but I did use Shizuku for some accessories on a few devices. It's a bit of ado to setup; not difficult just a handful of steps. Worth it if you really need or want to do something the GUI won't provide and you'll likely find more uses down the line.