Not a car but since you're a bike guy as well.
Just rebuilt a 1959 BMW R69. Motor has great compression, starts on the 1st or 2nd kick. However when first starting if I idle for a while it'll blow out a lot of white smoke(oil burning).
About 800 miles on it since the rebuild. Running SAE 40w oil as recommended by the manufacturer.
Is there a possibility the rings still haven't seated properly?
The rings seating (or taking a long time to seat) can also depend a lot on how the bores were prepared as well - clearance and proper cross-hatching can make a big difference. But I'd give it at least 500 more miles to see if they seat. It's hard for a rebuilder to get clearances as accurate as a factory build - and back in 59, a lot of factories didn't get things up to modern standards - back then every car and bike had to be carefully broken in over minimum 500-1000 miles.
The "white smoke" statement bothers me - if it's oil, it should be gray smoke. White is moisture - a big problem in seldom-ridden bikes. What do the plugs look like? Is the oil level going down?
Oil on threads on the one cylinder, but it smokes from both? This may seem like an odd question, but are you parking it on the side stand?
Here's a link to a shop my friends have found helpful with BMW questions/problems: https://www.maxbmw.com/
https://shop.maxbmw.com/fiche/DiagramsMain.aspx?vid=48042&rnd=09082020
Yes, bu they should have seated in by now. Hopefully, whoever rebuilt it properly staggered the ring gaps so they don't line up.
plugs look good a nice light brown in color but the threads on the left cylinder are oil coked.