Utter is installed from this site, not the Play Store. Android is extra careful with apps from the web, so it asks you to say yes twice: once to install, and once before the floating mic can be switched on. Both take under a minute, and you only do them once.
Rather skip the second step?
The Utter voice keyboard needs no extra permission. Turn it on in Utter's Setup (step 4) and switch to it whenever you want to dictate. You can still set up the floating mic later.
Samsung phones: Auto Blocker
If nothing happens when you open the file, or Samsung says the install was blocked, Auto Blocker is on. Open Settings → Security and privacy → Auto Blocker and switch it off, install Utter, then switch it back on if you like. Utter keeps working either way.
Utter walks you through these steps in its Setup tab too.
Why does Android ask?
The floating mic uses Android's accessibility access: it needs to see where the keyboard is and type the words into the box for you. Since Android 13, apps from outside an app store must be allowed this by hand, because harmful apps have misused it. Utter only uses it to place the mic and type your words into the box you are in. Nothing on your screen is ever sent to us. The pictures are from a standard Android phone; Samsung and other brands word some screens a little differently.