I agree with Kris, if the choice of "Convert to APFS" is greyed out, that format is already functioning.
However, to answer your question: "And how do I know when I am in Recovery Mode or not?"
In my opinion, always use the complete Shutdown and startup process instead of the "Restart" function.
So:
1. Shutdown the Mac.
2. Wait 23 seconds.
3. Hold down the Command and the "R" key with one hand.
4. Press the power button with the other hand.
5. Be patient. Keep the Command and "R" key down.
6. You will probably see the Apple Logo pop up. However, it may only be brief.
Keep the Command and "R" key down.
7. You should now see a progress bar. There may not be an Apple logo at this point.
Keep the Command and "R" key down.
8. The progress bar may only get to about 20%. Keep the Command and "R" key down.
9. The short progress bar wil be replaced by another progress bar with the Apple Logo.
10. You can now release the Command and "R" key.
11. You will eventually see the following:
A. A black background screen
B. A smallish window with a list of four items:
a. Restore from Time Machine
b. Reinstall (an operating system)
c. Safari
d. Disk Utility
12. Click "Disk Utility" (either with a double-click or just once and then use the "Continue" button)
13. Select any Volume shown.
14. Select The Edit menu and see if the "Convert to AFPS" is allowed.
A. If it is allowed you can convert that Volume to AFPS.
B. If that option is greyed out, the Volume is already formatted as AFPS or it is damaged.
If you don't see the steps above through #11, you are NOT in Recovery mode.