The 1 5/8 x 3 5/8 hasn't been used for 40 years. It's been 1/2 x 3 1/2 for years now. 1x lumber used to be 13/16 also.Never found any in the usual places, but I bet you can find a big lumber supplier who will have it or can order it. I live in the desert now, and my supplier is an hour's drive away, and so far as I know, they only have Baltic Birch ply in metric, 5x5 feet square.
l think 2x and 4x is actually 1 5/8ths and 3 5/8ths, which is to say 41.28mm and 92.58mm. To confuse us all even further, lumber is sold by the board foot, which is 12 inches square by one inch deep. Don't know how they sell it in metric countries, but the metric equivalent is 304.88 mm square, by 24.50mm.
Out in the shop I have a mesuring stick that's one meter long, with both metric and Imperial numbers on the same face, so I can, if needed, just look and see how long a metric measure is in inches and feet. I do think metric is easier in most ways, but I can't visualize a meter and think of it as a "fat" yard.
I found this on the web. It's a conversion chart. Detailed down to 32nds of an inch.