How might Earth’s axial tilt alter global wind patterns?

It probably would do little to high level patterns which are primarily driven by Coriolis forces while surface and mid level winds are governed by location/distribution of land masses Tectonic plate movement of the continental land masses and their distribution either towards each other or away as is the case today, are the prime drivers of wind patterns. at the surface and mid level so far as I recall.

Tilt angle migrates millions of years per degree the largest tilt being deducted from the geological record was 51° during the existence of Pangea during the Permian 250mya(?). I defer to a geophysicist for anything more specific. It would be difficult to estimate the contribution each component makes to wind patterns without running a simulation. And a simulation needs some seed data to evaluate.

Bottom-line: I am "inclined" to believe that tilt has little affect on prevailing wind direction. If we look at other tilted planets we see that their prevailing winds are always parallel to their equators regardless of their tilt angle from the ecliptic plane.