Why did the cost to make a backup spellbook go from 10 gp/level to 50 gp / level?

It didn’t 

copying your existing spell book costs 10gp/level

copying a new spell into your book costs 50gp/level

if you have lost your spellbook you can write down your current memorized (prepared) spells at 10gp/level and every other spell needs to be found and transcribed again at the cost of 50gp/level

That's not what UA says. To copy a known spell unto a new spellbook takes Scribe Spell, which costs 50 gp/level.  10 is never mentioned/