[Enhancement] Bind `profiler.firefox.com/uploaded-recordings` to Mozilla SSO.

I frequently switch browsers, OSes, and hardware. Consequently, I always authenticate with my Mozilla account, to ensure that my preferences are synchronised. However, [the list of which performance profiles I have uploaded](https://profiler.firefox.com/uploaded-recordings/) [^1] does not benefit from this. Consequently, tracking which profiles I have uploaded is difficult. If the list of mere URIs were synchronised to my Mozilla account, this would be a trivial endeavour.

[^1]:

I believe that this matters, because profiles tend to include private information.

┆Issue is synchronized with this [Jira Task](https://mozilla-hub.atlassian.net/browse/FP-1251)

Begin with the profiler.firefox.com/uploaded-recordings page described in the issue and the linked Jira task FP-1251. Trace how the uploaded profile URI list and Mozilla SSO are currently handled; done means the list follows the user's Mozilla account across browsers while preserving the stated privacy expectations.

Written by the indexing model from the issue text.