First, make sure that you have a Profile for Illustrator in the Actions Ring configuration page:

(Open the Logi Options+ app > Actions Ring section > select Illustrator at the top right or Add it as an Application)

Open Illustrator, then go to Window > Extensions menu and make sure the Logi Options+ plugin is selected. If the Plugin is not selected, go ahead and select it and accept the Security pop-up message. Once you select the Plugin, the “Logi Options+ Plugin dialog” should appear.

In some cases, you will notice that a “Warning” icon appears on some of the actions. This is because the action is not “actionable” with the currently selected object(s), e.g. if you want to use “Text size” action, you will need to first select the text you want to edit and then open the Actions ring.