Welcome to our community and thank you for your question.
In general you have to stay in your city/federal state for the first 3 years of your residence as long as you get social benefits from the state. Having a job or starting an apprenticeship/studies allow you to move.
You can move to another city (in NRW or another federal state) if you have a job there. It has to be a job where social security contributions are mandatory. You have to work in this job for 15 hours per week (or more) and earn 710€ net wage (or more).
The usual procedure is that you show your work contract to Ausländerbehörde. They will contact the Ausländerbehörde in the region where you want to move to and come to an agreement whether they allow you to move or not. If they allow it, they will remove the so-called "Wohnsitzauflage" from your documents.
In you case, however, it seems that it could be a problem that your company is not located in the city you want to move to. I coulnd't find a clear statement in this regard, but it looks like "Wohnsitzauflage" only gets removed in order to enable you to start your job somewhere else. Since it's an online job they might deny your request because you can do it from anywhere - including the town where you live right now.
I will link @Marcel in this case because he is a lawyer that is experienced with labour market access for refugees. In addition, maybe @DavidJ from Workeer or @stefan_J4R from Jobs4Refugees know something about the legal aspects of this case as well.