How does Magic handle “Type – Subtype” lines that don’t fit on the card when translated?
Generally—they just make the font size in the type line really tiny.

Some good examples are the Titans from Theros Beyond Death, which are Legendary Creature — Elder Giant. I've included other Giants in that search result so you can see that they just shrank down the font size a lot on Kroxa and Uro. They did the same for Thryx, the blue legendary card in those results, who is an Elemental Giant.

Here's three white cards in Russian side by side so you can see how much the font size might vary:



(Also the vertical alignment varies too apparently, probably for lack of attention/care rather than for any good reason. Oof.)

That's not limited to Russian, either. Here's some German cards undergoing the same treatment, where the middle one doesn't need any font size adjustment: