Can I apply for a worker visa after asylum?

I can't see how a 2nd asylum application will HELP the chances of getting a work visa. If anything, it's going to raise more suspicion on you AND the employer. You have already been denied asylum once, changing your address in your home country does not change the circumstances. You claim you were in danger, but then you didn't hesitate to return after the decision without appeal. You even wrote that you "didn't want to go back to your country", wherever that is. That tells a lot.

I think IGI is going to see that you are trying to "play" the system, which is shameful given that there are genuine people in danger seeking asylum all across the EU, including from neighboring Ukraine. What happens even if you do get the work visa and again, don't "get along with your employer"?

Those given asylum have the right to work, that's not a problem. Those given a work visa have a right to work, and that also is not a problem. What you seem to be doing, is a problem IMO.  Simply not wanting to live in your home country doesn't give you priority over other lawful asylum/job seekers.