My daughter was like that, and so is my friends daughters.
For us, we "let" my daughter wake up according to HER rhythm and timing. We "learned" to not rush in or pick her up or even to talk... until she was ready to interact. As she got older, she grew out of it... and then would actually tell us that us interfering in her "waking" was just irksome. She explained she needed her own way, to wake up... and to wake up fully, then she was "ready" to engage.
If we "rushed" her out of it... it just triggered her negatively.
Lots of kids just do not wake up very "happy" or pleasantly. My sister was like that too. Many people just are not 'morning people' or what not.
And yes, read up on "Night Terrors"... online. It is developmental based. And yes, it can last more than 6 months.
Try to go according to your child's rhythm... if she does not want to be picked up or held right away, then don't. It is her "telling you" what she needs, at that moment.
For my daughter, from a deep nap.. .it would take her about 1/2 hour to fully become "perky" again... and she just liked to have quiet... and her own "space" upon waking. BUT... like your daughter, she liked our "company"... in other words, just knowing we were nearby or in the room with her... just like a lamp. Then when she was ready, she'd start talking to us and being her regular perky/fun self again. She was just not always a good "waker-upper". But now that she is older, she is not like that. She matured out of that "nap/sleep" TRANSITION upon waking.
It is them, "transitioning" from sleepfulness to wakefulness. Not every child, NOR adults... wake nicely or calmly or pleasantly.
My sister is like that, still.
Don't feel YOU "have to wake her" from her slumber. Let her wake in her own way. Letting her 'cue' you....
All the best,