Temporary Containers NEVER sends any data to external servers and it does not track anything. It only stores necessary data LOCALLY to provide functionality.
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.
- "Monitor extension usage and manage themes": Required to provide automatic interoperability with other Container Add-ons like Multi-Account Containers, Facebook Container and Containerise. This is the management permission.
- 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.
- cookies: Required to manage tabs based on the "cookieStoreId", which is the internal way of handling tabs in combination with the container feature.
- storage: Required to store and read preferences/options and data needed to provide functionality.
You can find tips for assessing the safety of an extension here and more general explanation about permission requests here.