Update a page when it has actually gone stale or when the search results and searcher intent have moved, not on a recurring date. The honest answer to “how often” is need-driven, not calendar-driven, because an update that changes nothing of substance is exactly the pointless churn the question is worried about.
The line between a worthwhile update and churn is whether anything real has changed. A worthwhile update fixes information that is now wrong, adds something the page was missing, sharpens an answer the results now demand, or responds to competitors who have raised the bar. Churn is editing the publish date, swapping a few words, and shipping it as “fresh.” Search engines are not fooled by cosmetic edits, and readers are not better served by them, so that kind of activity spends effort and earns nothing.
This is why a fixed cadence is the wrong instrument. “Update every six months” guarantees you will touch pages that did not need it and miss pages that went stale in week three. Some pages cover fast-moving topics and need attention often; some cover stable topics and stay accurate for years untouched. Tying the work to a timetable detaches it from the only thing that justifies it, which is that the content no longer does its job as well as it should.
What you want instead is a set of triggers. Has the underlying information changed? Has the intent behind the query shifted, so the page now answers a slightly different question than searchers are asking? Have the competing results gotten meaningfully better? Has the page started slipping in rankings or traffic? Any of those is a real reason to update. None of them is a date on a calendar.
For each page you are tempted to refresh on schedule, stop and name the substantive thing that has changed since it was last touched. If you can name it, update. If you cannot, leave the page alone and put that effort where staleness has actually set in.