Ugh. I just wrote you a long post that's delete itself as my MN page refreshed. Bloody thing.
The gist was that I have an autistic 14 yr old DD who lies about the most weird and wonderful things, not always to gain an advantage.
It's about feeling too overwhelmed to communication, wanting an easy solution to a situation, and feeling anxious. Put her on the spot by asking her if X happened, and she'll deny it.
With your DD, what struck me is that it doesn't sound as if all of those scenarios need "punishment". What's your relationship like with her in general? You're in new territory now too as you try and navigate having an older child, maybe having a different approach would help you both?
In our house we don't have punishment, but we do have natural consequences. So for sneaking the tech into her room, the natural consequence is that every night it's handed to you before bed. That's the consequence of trying to sneak it in.
Personally, I don't think I'd be too bothered about her pinching clothes. I'd be inclined to approach that with humour. I don't think that warrants punishment of any description.
Also, I don't approach my DD with questions about what she's done. That means she has to "admit" her wrongdoing and that's just never going to happen. I find it better to approach it as a matter of fact where you're not seeking a confession from her, but demonstrating that you know and asking for the resolution (whatever that might be). "I see you've borrowed my blue top - can you drop it into the laundry basket please as I need to get to wear it on Tuesday". Don't get drawn into discussions or enter into debate - you're not interested in the lies, focus on the outcome.
I've found the trick is just not to give the lies any oxygen. Ignore them or treat them as a bit of a joke. Focus on positives, and stay matter of fact. Question whether every misdemeanour really needs "a talk" - teenage years are tricky and children are trying to figure out who they are while simultaneously feeling overwhelmed by just about everything. It's not about exerting your authority. Sometimes teens do annoying things, but not every annoying thing warrants a big pow-wow or punishment.
Finally, my DD communicates WAY better via WhatsApp. It takes the difficulty out of communicating, removes the anxiety and makes it feel less confrontational for her. You could try initiating simple conversations via WhatsApp?
None of what you're describing needs to be a big deal. Take the heat out of the situation and it might feel less stressful for both of you.