The German authorities for work permits do not care where you work exactly (assuming it's somewhere inside Germany). For some jobs, you might not even have a fixed office workplace. But a work permit is a work permit.
Especially with COVID on everybodies mind, remote work has become normal, sometimes even mandatory for periods of time as dictated by the COVID rules of the state.
Your physical workplace is mentioned in your contract, because that is where your employer can expect you to be while working. Allowing you to work somewhere else does not need a change in contract, it can be a simple policy. As long as both parties are fine with it, you can work remotely. A change in contract is only needed to guarantee you, that you can work remotely, even if your next boss doesn't like it or the company tries to change their mind.
You should have no problems with your working contract. Either you sign a new one, more likely it's simply a change in contract that both sides sign. Nothing else changes, just the physical workplace. If you sign a completely new contract, you may need to notify the "Amt", but that is just buerocracy. Like I said, they don't care where you work.