  We propose entangling operations based on the energy curvature couplings of
encoded spin qubits to a superconducting cavity, exploring the non-linear 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
$\sigma_z$-coupling, offering gate times of 10s of ns even when the qubits and
the cavity are far detuned. No dipole moment is necessary: the qubit transverse
$\sigma_x$-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 "dispersive-like" static
curvature coupling), most of them associated with the non-zero qubit energy
curvature (quantum capacitance). Using spin-echo-like error suppression at
optimal regimes, gate infidelities of $10^{-2}-10^{-3}$ 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.
