Upgrading gears from microshift to Shimano
Even cheap components should shift okay-ish, unless they are badly worn.
Shifting problems are usually caused by any combination of:

Bad adjustment: Incorrectly set cable tension or limit screws.
Excessive cable friction: Due to bad routing, worn cables, worn cables housing, missing/bad cable housing end caps or very low-quality cables.
Bent derailleur hanger. Look at the derailleur cage from behind the bike, it should be parallel to the center line of the bike.
User error: Don’t shift under (high) load. Don’t shift in a standstill.
Worn components. Usually the chain. You should replace the chain early enough, when it’s 0.75% stretched. This will typically be after 1000 to 4000km, depending on conditions. If you do so the cassette and chainrings can last more than 10000km. The derailleurs can also last more than 10000km.

Have you ruled out all of those? Only then would I think about a replacement/upgrade.