Felipe bunq is a Dutch bank, all accounts (regardless of the country IBAN) are Dutch bank accounts. Only German banks that have special contracts with SCHUFA provide information to them, and mostly only because of the necessity to get information about a customer themselves. At bunq this information is not needed, and most customers probably prefer to have their bank share less information about them with third parties rather than more. Especially bunq has a strong privacy stance where services like SCHUFA just doesn't fit into.
When it comes to your landlord, they are a private person or company and can therefore freely decide who to contract with. If they deem it necessary for you to have a bank account with a bank that shares your information with a certain third-party, then unfortunately I don't think bunq can really help here. Of course, you can always export your bank statements from the past which would show your income and expenses and opt to share this information with them.
That being said, a normal SCHUFA report doesn't actually have any detailed information like this in the first place even when you're banking with one or multiple banks that do provide information to SCHUFA. The only thing it would mention is if you have any outstanding debts that you haven't repaid on time, so in most cases less entries in your SCHUFA data are actually a very good thing. The system here in Germany is different from for example the US, where you "level up" by having certain good activity. Here you almost exclusively can only "level down".
Did you try submitting your current SCHUFA report to the landlord? Was it declined explicitly because of bank account information?