I very much relate to the OP and experience frequent morning anxiety right after waking and recurring anxiety dreams as well along with lingering panic upon waking. The morning pattern is actually quite well-known to relate to normal daily fluctuations of cortisol and other chemical levels, which tend to peak at that time. Google "morning anxiety cortisol".

For me, it helps me to know it is primarily just how my brain interprets chemical fluctuations and it is best to ignore it as it goes away pretty soon after I get going and as the day progresses, however uncomfortable and confusing initially. It really sucks but, I think, it is better to try to recognize it for what it is primarily: a physical condition affecting emotional regulation.

One thing that made this pattern of my anxiety much much worse in the past was drinking alcohol and being hungover (that's where the anxiety tended to be the worst), it's much more mild now that I don't drink at all. Cutting down on caffeine and forcing myself to eat some healthy breakfast (to eliminate the anxiety-increasing effects of low blood sugar) also help.