TLDR; Tranquility Reader does not collect or transmit any information to an external website.
From its very early versions in 2012 as a legacy addon, the aim of the extension has been to respect the privacy of the user.
It was developed as an addon/extension rather than as a web service explicitly for this reason (in contrast with other applications like Instapaper, Evernote etc. which either processed the webpage on their remote servers, or stored the transformed page on their remote servers or both).
For the above reasons, there has never been and there is no plan in the foreseeable future to process or store any information outside of your browser/computer. In the unlikely even that such a change is necessary, this will almost certainly happen as a new/separate extension.
Tranquility Reader modifies a web page locally on your browser by modifying/deleting/hiding elements on the original web page.
As a part of its working, it can stop loading a partially loaded page and re-fetch the page before modifying it.
The extension stores your preferences/settings locally on your browser. Similarly, if you choose to save pages for reading later (offline), it stores such offline pages in your browser (local storage).
For Mozilla's end user friendly explanations of the different permissions please refer to this page.
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"activeTab": Modify data on the current tab (required when running the extension to modify the web page and make it readable).
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"storage": Store user preferences and offline pages locally on your browser.
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"alarms": A way of giving visual clues (with built in time delays) to the user when preferences have been updated successfully (or if there are errors).
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"contextMenus": Allow for the "right-click" menu options on desktop version of the browser. This lets you process and load a link in a new tab, highlight text and transform just that portion of the page, or add annotations.