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Jonny69
nogk
c*j*f
https://www.sheldonbrown.com/cribsheet-headsets.html
If the stem/quill is 28.6mm (1-1/8"), then the steerer inner diameter will be the same and the steerer outer diameter will be, as you say 1-1/4" or 31.8mm.
I imagine a straight adapter is available, just the usual is 1" to 1-1/8".