I’m gathering that the logo container is square? Is that correct?

First of all, a logo should be designed in a vector application.

Secondly, the size should generally be pretty big (e.g. 4000x2000px), because you might want to use it in different places, like social media covers, ad banners, or perhaps you want to print it on a shirt or something :D, and so on.

Being big, you can scale it at any size you want.

When you add it on your website, you should scale it to a proper size, depending on your header and design. A landscape aspect ratio would be best, because a square could stretch your header too much vertically, but again, it depends on the logo and the site design.

Something like 200x100px would be good.