Ah yes, measuring out anything into thirds is awesome with metric. Nothing ever needs to be split into thirds.

When you buy a piece of lumber in Europe it’s cut to 45x95mm which (shockingly) converts to the absolutely nonsensical 1.77165x3.74016 inch two by four

Ah yes, nice round numbers there as well with metric. Why isn't it just 50x100mm? And that conversion is not even the imperial measurement of a 2x4, and you clearly don't understand where the dimensions come from.

There are nominal dimensions, and actual dimensions for lumber. The name 2x4 is the nominal dimension, the rough size before drying and planing. Between the forest and the hardware store, a board loses material twice.

1. A log goes through a sawmill and gets cut into rough boards. At this point, a 2x4 really is about 2" x 4". Green (freshly cut) wood contains 30% or more moisture.

2. The boards go into a kiln where hot air drops the moisture content to about 19%, as water leaves the cells, the board shrinks. The dried boards are rough and uneven. A planer shaves all four sides smooth. S4S (Surfaced Four Sides) means all four faces are planed. The planer removes another 1/8" or so from each face.

Result: a board that started at 2" x 4" ends up at a standard measurement of 1-1/2" x 3-1/2".

Now to get back to the metric equivalent... that 45x95mm board... starts with a nominal dimension of 47x100mm. Neither the nominal or actual dimensions are nice round numbers here, although at least the actual dimensions at the end are a multiple of 5. Why some places also refer to these as a 2x4, well they're the equivalent even though the actual size is completely unrelated.
UK example