Temporary Containers asks for permissions upon installation:
"Access your data for all websites": Required to provide automatic reopening of websites in Temporary Containers. In order to do that, it is necessary to be able to intercept and potentially cancel every request inside the browser. This is the all_urls permission in combination with the webRequest and webRequestBlocking permissions.
"Access browser tabs": Required to access the tabs URL, which is also needed to provide automatic reopening of Websites in Temporary Containers in cases where the currently loaded URL in the tab is relevant to decide whether to stay in a container or open a new one. This is the tabs permission.
"Management": Required to provide automatic interoperability with other Container Add-ons like Multi-Account Containers, Facebook Container and Containerise. This is the management permission.
More required permissions included in the Add-on that don't show up as special text when installing the Add-on are:
contextMenus: Required to add the context menu entry when right clicking links.
contextualIdentities: Required to use the container feature itself, which is natively available in Firefox with this permission.