Without the use of a mod to provide multiplayer island management and creation, we have to rely on Botania’s own mechanism to create them. This page and the other I have here at kreezcraft.com would not be necessary if the Botania wiki would have this data.
I have tested the following information on 1.16.4+ and even other prior versions too, and it works reliably. No matter how many people log on, no matter how many times they smack that button, it remembers the island for each person.
The command you need to enter into a the command block is
You will note that the command is different from the image, I have adjusted it for 1.16.5. The @p is simply the nearest player. The r=3 means a radius of 3 from that command block.