The phrase full-time musician covers a dozen different financial arrangements. Some people earn most of their money on stage, some from sync placements, some from teaching four days a week so the other three can be spent writing. None of these is more legitimate than the others, but they carry very different risks.
Live income is high variance and front-loaded with costs. Streaming income is small per unit but arrives predictably once a catalogue is large enough. Teaching and session work are steady but cap out at the number of hours in a week. Most sustainable careers combine at least two of the three, precisely because their weak points do not overlap.
What tends to separate people who last from people who burn out is not talent but cash-flow awareness. Knowing that a tour will be paid ninety days after it ends, or that a quarterly royalty statement covers activity from six months ago, removes an enormous amount of unnecessary panic.