Why so much variance in the continuity beeper threshold? How do these beepers work anyway?
The reason the range is so large is that few people care what the range is.

The 'continuity beep' is a 'nice to have' feature, not an essential feature. It doesn't do anything that can't be done on the ohms range, albeit avoiding the need to read the display.

When a large enough segment of the market starts demanding continuity beep thresholds with a tolerance of x%, then the manufacturers will start specifying and providing them.

Test is a significant part of the cost of making equipment. If a feature doesn't need testing, because it's not accurately specified, then that feature can be added very cheaply.

The reason the ABC company might add a continuity beep function is that XYZ company have one on theirs, and we don't want to lose out on a sale when customers hold the data sheets up side by side and do a comparison. "1% on DC voltage, check, at least 1000v, check, continuity beep, check!" If there's no standard, it just doesn't get standardised.