New Landlord Trying To Raise Rent Despite Signed Lease

I’m dealing with a frustrating situation and could really use some advice. I recently signed a lease with my previous landlord, locking in the rent for NEXT year (this year is no problem). However, the landlord sold the building to a new owner shortly after, and now the new landlord is telling me they won’t honor the rent amount in the lease for NEXT year. They’re saying I need to pay more, but my lease clearly states the agreed-upon amount.

The lease also has this clause:
"The Landlord and the Tenants are bound by this Lease. All parties who lawfully succeed to their rights and responsibilities are also bound."

I’ve tried explaining this to the new landlord, but they seem firm on raising the rent. I’m worried about what to do next.

Has anyone dealt with something like this? What are my rights here, and how should I handle this? For context, I’m in NJ.

Any advice or suggestions are greatly appreciated!