Can an introvert thrive as a Service Designer?
In short: yes. Many Service Design professionals are introverts. In fact, I'm one too.
I'm rather on the side of introverts. Being with people costs me more energy than it gives me back. I'm someone who is happy being alone. Still, I'm working for years as a service design practitioner.
Introverts to me, are good at feeling the emotions of others, and that's something extremely useful when you conduct interviews, do user testing or run a workshop.
So I would say if you are not an extreme introvert who never wants to speak to anyone, then a career in Service Design is perfectly possible for you. And as with any personality trait, you'll have advantages that will make the job easier and disadvantages that you'll learn to manage.
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In short: learn to deal with negative feedback, give enough time for life and learning, keep track of the good stuff, and don't forget to sleep.
Can a service designer survive a recession?
In short: Yes, if you can also provide a lean and low-hanging fruit approach that is focused on the present. No, if you are "only" focused on long-term strategic work.
What are tips to become a senior service designer?
In short: mentor others, teach others, try out new technics.