I mean, I dunno about other stuff, but this? Is easily explainable.
Symbie is an artificial intelligence build from designs of an advanced space-dimension-faring race. She is actually more similar to QA than Taylor. That's not even saying anything about what Queen Administrator could have granted her access to simply by accident of her creation. No, seriously, children of Shards usually constitute components of their bodies with various levels of access to the overall functionality. Taylor is more like a sister, I guess? A very depressed and drunk sister slumming it in your crystalline matrix until she feels better, only to find excuses not to feel better because she actually likes it here, you know how that goes.
What I'm saying is Taylor has to actively suborn Queen Administrator's functions, even if she doesn't mind and actively encourages it. Symbie doesn't seem to even need to ask permission, the automated systems already treat her like she belongs here, because she actually does.