@LeroyG yes but once Header (and Footer) has initialised, it is “frozen” in this configuration. It is impossible to handle mixed layout, both portrait and landscape orientation in the same document, with only built-in Header. You must create new paragraph style for the other orientation.
OP didn’t mention if the whole document is landscape (in which case your observation solves the issue) or is mixed (needing two or two sets of paragraph styles).
Personal comment: this illustrates the shortcoming of our mechanical typewriter-era cultural legacy. Tab stops are only considered relative to origin of reading direction (because typewriter carriage could only move so).
With sophisticated layout possibilities offered by “modern” technology, we should redefine tab stops as being relative to some user-chosen origin: left indent (reverse for RTL), right indent or more generally some percentage of either page width between margins or paragraph width between indents.
For example, origin 0% if at left “edge”, 100% at right “edge”, 50% at centre. Stop distance is relative to this origin, positive in reading direction, negative otherwise (therefore allowing for a stop at left of indent when first line is hanging).
Of course, this seriously complicates sorting stops because we have a mix with different origins. The UI should show them sorted by absolute distance while allowing to tell which origin is referenced. Internally, all stops are converted to “absolute”.
Updating a style is probably not more difficult than now. But the acute problem is stops become context-dependent. Take the example of Header where we redefine the stops as (50%, 0cm) = centre and (100%, 0cm) = right, indents 0cm, 0cm. It is obvious that the absolute distance, counted as usual from left, is not the same in a portrait or landscape page of same size. How can this be simply solved? What is the impact of changes either in page style or paragraph style on reflow performance?