The tenant's counteroffer represents a rejection of the landlord's proposal for extension of the lease -- which means that unless the landlord is willing to give them another chance to accept, their principal option is to move out at the end of the current lease term.

They cannot impose a different rent increase on the landlord by suggesting that non-response is consent or agreement. If they want to negotiate the rent, they should contact the landlord and enter into an actual negotiation. If they stay into the new lease term without negotiating a different rent than the increased amount stated by the landlord, they should expect to pay that full amount.