Employer threatening to sue over non-compete - I thought these weren't enforceable in California?

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Illustrative scenario prepared by my practice.
For informational purposes only. This is not legal advice. Employment law situations require individual assessment.
Hypothetical question

I'm freaking out. I just accepted a job at a competitor and gave my two weeks notice. Today I got a letter from my current employer's lawyer saying I signed a non-compete and they'll sue me if I join the competitor.

I work in tech in San Francisco. I thought California banned non-competes? But their letter cites a bunch of legal stuff and says I agreed to be bound by Texas law (company HQ is in Austin) sadly.

The non-compete says I can't work for any competitor for 2 years after leaving. That would basically end my career in this field. What do I do?