The bug

The game saves natural enchantments as shorts, yet using integer values (eg 32768 (max short + 1)) makes the game load them fine as integers numbers.
Note that the enchantment saving and loading logic exists in multiple methods which all behave differently.

20w07a Mojang names:

• ItemStack.enchant(Enchantment, int): Casts the int enchantment level to byte (-128 to 127) and then stores it as short
• EnchantmentHelper.setEnchantments(...): Casts the int enchantment level to short (-32768 to 32767) and then stores it as short
• EnchantmentHelper.getItemEnchantmentLevel(Enchantment, ItemStack): Reads as int and then clamps it to 0 to 255
• EnchantmentHelper.deserializeEnchantments(ListTag): Reads as int
• EnchantmentHelper.runIterationOnItem(EnchantmentVisitor, ItemStack): Reads as int
• EnchantedBookItem.addEnchantment(ItemStack, EnchantmentInstance): Reads as int, then writes as short
• ItemStack.appendEnchantmentNames(List<Component>, ListTag): Reads as int

How to reproduce

1. /give @s stick{Enchantments:[{id:"sharpness",lvl:32768}]}

2. Close and reopen the game
   Note that the enchantment level was loaded just fine
3. Put the stick in an anvil and rename it
   The level overflows and becomes -32768