Noir does not collect any of your data. The only data the app stores are your settings. These are only saved locally, and optionally in your own personal iCloud account. No one, other than you, has access to this data.
Because of the way Noir works, the Noir extension needs to have permission to access every website. This is needed because Noir has to analyze the existing style of a website, and override it with Noir's dark style. However, Noir will never use these permissions to actually read the websites you visit, or to access your browsing history. Noir does not store any information about the websites you're visiting. Not even locally on your device.
If you decide to report an issue with a website through the app, that report is then sent to a server, and stored in a database that only I, the developer of the app, can access. The only information that is stored is: the (sub)domain of the reported website, the full URL of the page if you optionally included it, the category of the issue, your description, the version of the app and the kind of device (iPhone/iPad/Mac) that you were using, and an anonymized hash of your IP address.
If you have any additional questions or remarks, feel free to reach out to me! You can reach me at firstname.lastname@example.org.