The difference in power is mainly affected by the effect size and number of samples and not by the number of proteins measured.
The following number of samples is needed to reach 80% power in a two-group comparison (two-sided two-sample t-test) with 1500 proteins. With a moderate effect size (delta 0.5), you need to have around 55 samples per group, with a small effect size (delta 0.2) you need around 320 samples per group.
A study with 1 full plate (44 vs 44 samples) reaches a power of 64% for a moderate effect size when measuring 1500 proteins. As a comparison, when 1000 proteins are measured instead of 1500: One full plate gives 67% power for a moderate effect size => the difference in power is not big (64 vs 67%).
Conclusion: It is the effect size and number of samples, not the number of proteins measured, that mainly influences the power. See the power simulation figures below: