If other ranges is out of specification I don't know.
You probably did this all already, but if your Chinese ref standard is correct at 2.49939, then the Brymen showing 2.521 is out of specification.
Brymen BM257S spec is 0.2% +3d in all DCV ranges.
2.49939 x 0.002 = 0.00499878
2.49939 + 0.00499878 = 2.50438878 => 2.504 + 3 digits = 2.507 (high end bound)
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If your Chinese ref standard is correct at 5.00143, then the Brymen showing 5.045 is out of specification.
Brymen BM257S spec is 0.2% +3d in all DCV ranges.
5.00143 x 0.002 = 0.01000286
5.00143 + 0.01000286 = 5.01143286 => 5.011 + 3 digits = 5.014 (high end bound)
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So it looks like your 6V range is out of spec.
The interesting question for Brymen is how the meter knows there is a Calibration error? Maybe during bootup, the main IC can't read the calibration constants/offsets and thus reports calibration error?