I think $2k is a reasonable budget given you are just getting into this. Like most watches and cars bikes take a big hit once you take a new one out of the store so keep in mind that with this budget you could get a lot more bike by going used. Check out The Pros Closet, and there are other similar business offering used bikes and equipment. Also keep your eyes open locally, there is bound to be a lot of folks in your area flipping bikes quickly to upgrade.
The electronic shifting is standard in those higher end / priced bikes you mentioned but it gets introduced at a lower price point actually. It is however unnecessary and like all components can be added later.
I’d be looking for a carbon frame bike, with disc brakes. Road bikes these days run up to 28mm tires, the gravel bikes maybe up to 40mm. I don’t think you’ll have to worry much with 28mm on the LA roads.
You should be able to get a new bike, carbon, hydraulic disc brakes for around that number. All the big brands will have bikes at that level. And honesty, what you get for $2k today is pretty good. Buy last years bike, or the year prior and get a decent discount. You need to look closely but often the differences are minor.