Spelloyal

The available teigus are mostly so-so, with one or another being extremely useful like the Wings or the teleportation one, but the technique to create Teigus would be incredibly valuable to someone with access to dungeon materials or the multiverse with beasts and materials available everywhere.

This is actually a recent problem. The empire only declined due to the death of the previous emperor and the corrupt prime minister taking control of the new emperor, along with the great powers of the empire such as General Budo being extremely loyal to the empire without caring about corruption.

The empire does not rule the world, in fact they would be screwed if it weren't for the country that still knows how to produce Teigus not being unified at all.

Normal people in this world don't get that strong, most high-level fighters are Teigu users, have undergone genetic experiments and modifications, or use extremely rare special techniques. Even Teigu users aren't very strong in general, there are only 4 or 5 really strong ones. But the Teigus themselves have a lot of potential if the MC learns how to make one.

Except for creating teigus, there is nothing really useful in this world. But if Mika learns how to create teigus, it will be amazing since they are basically a prototype for sacred gears. Luckily, there is a country where the method of creating teigus has not been lost.

In the nasuverse there is a family of Magus specialized in making artificial magic eyes, it should be possible to use this eye to create a very powerful magic eye.

In reality, she's probably farming excelia in the dungeon and leveling up with blacksmithing achievements, since she's the best blacksmith in Orario. The fact that she's taking a risk by being the test subject for new weapons probably also increases her excelia, since she must take a huge risk whenever a new experimental weapon breaks in the middle of a fight. She'd probably have a much harder time leveling up otherwise.

The problem with the Tower and the Tower of God universe in general is that it canonically operates on the concept of written stories. Like a book, the entire lives of the characters are predetermined from beginning to end, including the irregular ones. To put it simply, canonically it's all a story written by a god, including moments where the characters seemingly break their fates, so it's a terrible universe to visit without something like the Waifu Catalog defenses.

Having some muscles is cool, but Bodybuilding is too much and not good for fighting or healthy in general.

She actually does, she often uses a whip to fight and beat up mobs even without using magic, but she's nowhere near the level of someone like Natsu or Gray.