Bug report logs a timestamp but nothing happens to this automatically. There is no red flashing light that goes off in the engineering bay and suddenly all the developers drop what they're doing and investigate your issue. In fact it goes into a black hole unless you also call Tesla and convince somebody to take a look -- which I know from experience has gotten to be almost impossible now because their support lines are completely slammed. They don't want your bug reports, and they don't want your trouble tickets. If by some miracle you do get somebody to pay attention (probably by going through your service center rather than telephone support) then hitting that bug report button and making a note of the approximate time will allow them to find it in the logs.
But -- this is the key thing -- they are not going to care to do this unless the service center believes there is a particular hardware problem with your car. This is not how they fix software bugs for the most part. Believe me, they have more than enough examples of their software doing stupid stuff; they don't need your examples anymore.
That's the opposite of what Elon told us a few months ago, but I don't have any insight into Tesla's internal process to know either way.
Certainly the bug report is an easy way to document your issue and get it into a collection that someone may look at at some point.