A little known feature of many websites is what is known as a PWA or progressive web app. Basically what it means for you, the hexbear app desirer, is that on a mobile device, some web browsers will let you install the website as an app which will act like pretty much any other app. To do this, open up to any hexbear page and click on the menu. In Firefox there are three dots in the bottom right. You should see an option that says "install." Clicking that will basically allow you to view the website as an app, allegedly with better battery performance.
Is this the same as the chrome feature of "Add to Home screen?"
True. I'm a firefox user generally, I just wasn't aware of this feature.
some browsers will have a button for "add to home screen" but it's just a shortcut to a browser tab instead of a webapp (main differences is that it still opens the whole browser along with it)
Yeah, Firefox has the same option with the same wording if the website doesn't support it.
You can also use the iOS shortcuts app to create a home-screen shortcut that opens it in safari and that allows you to set the icon and title to whatever you want.