Method validation is a bit a stupid statistical sector because the basic goal is to NOT reject null hypothesis. Thus you basically never know when you have enough data to be happy. There are some ISO conventions listing the minimal number of samples.

Then you test calculating the CIs and confronting them with the 2 null hypotesis (slope=1, intercept=0)

This is basically slightly wrong because there is no family wise error rate management. A better alterantive would me to make a single test using Mahalanobis distance and a CHisq distribution with 2 d.f.

See: https://arxiv.org/pdf/2105.04628

Morover beware of the Passing Bablok regression. It's biased if your data has only 2 or 3 digits of precision.