Integrate cross-tab identity leak protection into Tor Browser with native UX

In response to the potential for cache side channel attacks reported in #41071 (closed), @ma1 deployed Cross-tab Identity Leak Protection (or "TabGuard") in NoScript 11.4.8. However some users are finding the warning confusing, and/or are suffering from warning fatigue – e.g.:

<Jeremy_Rand_36C3[m]> So far at least 2 users in #tor have been very confused about the NoScript warnings that were recently added.  One of them thought the warning meant his identity had already leaked, and panicked and shut off Tor Browser.  Seems like we should ask the UX Team to evaluate how we can improve this, now that we have some breathing room since the vulnerability is mitigated.
<Jeremy_Rand_36C3[m]> One of the two users I noticed who was confused about the warning was one of my co-workers, who is very technically proficient, including about Tor, and even he couldn't understand what the warning was about, what triggered it, and what the correct course of action was
<Jeremy_Rand_36C3[m]> Then you have a less sophisticated user who thought the warning meant he was already pwned and panicked
<Jeremy_Rand_36C3[m]> I was hoping the UX Team might be able to evaluate how this warning can be better presented so that users don't get confused or make bad decisions when they see it

We're planning on integrating this feature into Tor Browser as part of the work to migrate the Security Level feature in #40925. We should take this opportunity to improve the UX in general, in addition to converting the feature into standard Tor Browser UI patterns.