The eponymous '63 Rickert was used a lot with Challenge Grifo (now labeled Almanzo) clinchers that stretched out to a measured 35mm. Still good clearance all around. Was necessary to deflate rear tire to remove or install back wheel. That was a completely normal road bike. Tight spot with 38 would be the rear brake bridge. It would make it, not sure I'd do it. Real 35 as opposed to 35 label is a big tire.
Current 1950 Bates has older single spring Weinmann 750 with pad at bottom of slot. Stops fast. The Bates would not take 38. Or 35.
Look at older frames. Old means old. Not 70s or 80s production frames.