I'm a moderator in a server with Tatsu. I am the "bot guy" in that server, so i have the Manage Server permission and I am able to moderate bot thingies.
However, I cannot add items to the server shop. This is because there is no mod command that lets you do this but mainly because you have to have full admin perms to moderate the server via the site.
My suggestion is letting people with "Manage Server" perms moderate the bot via the website, because server owners rarely trust their moderators to give them full perms.