I am just fractionally smaller than the OP in both overall height and leg length, and I have no problem with 23 1/2" old school road frames with horizontal top tubes.
The only ones I have had to be careful with were an early 23 1/2" Raleigh Pioneer hybrid frame, with a high, MTB-inspired BB height, and this lugged 23" Raleigh MTB, if ridden on rough surfaces. The welded 23's have a slightly lower standover height and are fine.
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The early Pioneer frame cracked and has now been retired, the MTB isn't used as an MTB, since I've got others with more standover clearance better suited for that.
There seems to be a fashion these days for people to ride undersized bikes, which I find rather bizarre. Youngsters in my day often rode oversized frames on the basis they had "growing room" and so would last the rider until they stopped growing, but now I see the exact opposite - adults riding what I would consider to be kids sized bikes.