This blurb doesn’t specifically mention how low to mow. But it does give advice about when to mow.
The question is, after flowering, when to mow the lawn? Snowdrops may
not finish flowering until February/early March, depending on variety,
and meanwhile the lawn is ready for its first mow of the season.
Snowdrops are like all bulbs, as they die back the leaves feed the
bulbs forming for next year's flowers. If you mow the lawn, and with
it the snowdrop leaves, you will impair the leaves' ability to feed
the bulb and store the nutrients for next year.
In short, don't mow until the leaves have turned yellow.
https://www.sundaygardener.co.uk/how-to-plant-and-grow-snowdrops.html
Since the plants eventually die back, maybe it doesn’t matter how low the lawn is mowed, as long as I wait until the leaves are yellow.