I would agree with other posters saying take a few days off or a week, see if when you come back your legs are no longer sore.

In college I would help people with biking, a lot of people think their seat height is fine, I'd raise it, it would feel weird at first but within 2-3 rides they'd talk about how it was more comfortable and they were faster without more effort. However, your seat looks about as high as I'd want it to go on that frame.

This warmup/flexibility routine helped me be more comfortable on the bike, dunno if it would help your legs or not but it's a suggestion:
https://www.defrancostraining.com/jo...ility-routine/
https://www.youtube.com/watch?v=FSSDLDhbacc (video)

The answer to your question though is no, it's not normal for your legs to keep being sore after the first few weeks of riding. Usually the soreness goes away - first few times my legs were really sore, but after you get used to the exercise you can usually completely exhaust your legs to the point of having difficulty walking up stairs, and your legs won't be sore any more (unless you have arthritis or something). First thing I would try is taking at least a couple of days off from biking or any leg exercise (other than walking to the car) and see if your body fixes itself.