Ohhhhh boy!
Yeahhhh, any changes to intake or exhaust will change the behaviour of the bike. Increasing the amount of air in (For instance via K&N high performance air filter) or the amount of air out, such as after market exhaust, will have some effect. Typically it will cause the bike to run a wee bit lean as it’s now breathing better.
For starters, there is an Idle Adjustment thumb screw. You can adjust this to set the default idle to run a bit richer. It will idle high til it warms up to operating temps, but that is the quick fix solution.
https://www.manualslib.com/manual/1018449/Hyosung-Aquil-Gv650.html?page=24#manual
Depending on the increase of airflow due to after market intake/exhaust you might need to change your carb needle jets
If you really want to get into the weeds of carby tuning I found a tutorial from Marcel
[Tutorial] How to adjust Carb Slide Needle (Tuning) – Hyosung GV & GT 125/250
Honestly, the aftermarket slip-on should not make that much difference. It might cause it to run a bit lean, just as a high performance air filter would do. The quick fix, once all your other issues are sorted, is simply making sure your spark plugs are properly gapped, your air filter is clean, and adjust your idle up to run a bit rich
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