Generally, the Bankruptcy Court likes to be aware of any relevant and pending cases. The judge will decide if an adjournment is warranted in your situation.
Since you have filed in the Bankruptcy Court, your petition should state other pending matters. Regardless of whether you may voluntarily withdraw your petition, you should update the Bankruptcy Court by way of letter if there are any additional developments in the other case, including settlement discussions. On the other hand, the fact you are in Bankruptcy Court should be motivation enough to ensure the party in the other case provides you with reasonable settlement terms, as they are unlikely to do better in Bankruptcy Court.
Your bankruptcy filing postponed all other cases against you so without the bankruptcy judge's permission to proceed I do not believe th settlement can be approved. So yes you do need to inform the bankruptcy court and also file a suggestion of bankrupty in the other case
Any ongoing disputes or claims which can be satisfied by money must be disclosed with your bankruptcy filing, or immediately after it occurs, whichever is later.
I don't know what kind of dispute you're negotiating, but under the bankruptcy code, all actions (with some governmental exceptions) are stayed until the end of the bankruptcy, unless the judge allows some case to go forward. Understand that if you're negotiating payments either to you or from you, that case should not be going forward, unless the bankruptcy judge gave leave to you, or a creditor, relief from the stay. If that's the case, anything you negotiate in a settlement, if it's to be paid to you, will immediately become an asset of the estate, to be paid out to your creditors.
If you don't disclose all of this to the court, this bankruptcy court could dismiss your filing on account of fraud, and theoretically be prosecuted.
You need a lawyer immediately.
I am an attorney admitted solely in NY. None of the answers I submit on this forum constitutes legal advice, even to questioners in NY, and no attorney-client relationship is hereby created.