No wonder you guys are scared AI is going to take your job lol.
Thats not how it works at all. To grab a key stored in a JS variable, the following would need to happen
1. Attacker needs to find a way to inject arbitrary JS code in a website, which means controlling either an iframe that is loaded or some component. This is a pretty hard thing to do these days with Same-Site strictness
2. The code needs to know specifically what memory address to target. When things like JWT or other tokens are stored in session or local storage, the variable name usually contains a random string. Injected code will have to figure out a way to find what that variable name is.
3. For attack to work, the cache has to get evicted. This is highly processor specific on how well it works, and also, the web app has to be in a state where no other process is referencing that variable. With JS, you also have to infer memory layout (https://security.googleblog.com/2021/03/a-spectre-proof-of-c...) first, which takes time. Then you have to train the branch predictor, which also takes time.
So basically, I have a statistically higher chance of losing my keys to someone who physically robs me rather than a cache timing attack.
Generally when an exploit like this drops, people always have failures to update their systems, and you see it being used in the wild. With Spectre/Meltdown, this didn't really happen, because of the nature of how these attacks work and the difficulty of getting the cache timing code to work correctly without specific targeting of a processor and ability to execute arbitrary code on the machine.