We propose entangling operations based on the energy curvature couplings of encoded spin qubits to a superconducting cavity, exploring the nonlinear qubit response to a gate voltage variation. For a two-qubit (
n-qubit) entangling gate we explore acquired geometric phases via a time-modulated longitudinal ${\ensuremath{\sigma}}_{z}$ coupling, offering gate times of tens of nanoseconds even when the qubits and the cavity are far detuned. No dipole moment is necessary: the qubit transverse ${\ensuremath{\sigma}}_{x}$ coupling to the resonator is zero at the full sweet spot of the encoded spin qubit of interest (a triple quantum dot three-electron exchange-only qubit or a double quantum dot singlet-triplet qubit). This approach allows always-on, exchange-only qubits, for example, to stay on their ``sweet spots'' during gate operations, minimizing the charge noise and eliminating an always-on static longitudinal qubit-qubit coupling. We calculate the main gate errors due to the (1) diffusion (Johnson) noise and (2) damping of the resonator, the (3)
1/f-charge noise qubit gate dephasing and
1/f noise on the longitudinal coupling, (4) qubit dephasing and AC-Stark frequency shifts via photon fluctuations in the resonator, and (5) spin-dependent resonator frequency shifts (via a ``dispersivelike'' static curvature coupling), most of them associated with the nonzero qubit energy curvature (quantum capacitance). Using spin-echo-like error suppression at optimal regimes, gate infidelities of ${10}^{\ensuremath{-}2}--{10}^{\ensuremath{-}3}$ can be achieved with experimentally existing parameters. The proposed schemes seem suitable for remote spin-to-spin entanglement of two spin qubits or a cluster of spin qubits: an important resource of quantum computing.