[QL-Balance] Evolve and restart target-current shielding amplitudes

[krystophny]

What to build

Make the target-current shielding amplitude part of QL-Balance's accepted/trial time-evolution state for every periodic KIM mode. At each accepted profile state, refresh the unit local response, recalculate shielding current, update the amplitude, embed the scaled transport globally, and then advance the profiles.

Rejected time steps must restore both profiles and amplitudes. Restarted evolution must be indistinguishable from uninterrupted evolution.

Acceptance criteria

• Every mode has distinct accepted and trial complex amplitude state plus normalization diagnostics.
• The first accepted state begins with the documented constant-psi unit drive.
• Each response refresh uses the latest accepted global profiles and recalculates the unit shielding current.
• Fields and currents use the updated amplitude and diffusion tensors use its squared magnitude exactly once before profile evolution.
• The amplitude is committed only when the corresponding profile step is accepted.
• A rejected or failed step restores profiles, mode responses, and amplitudes to the last accepted state.
• Restart data preserves complex amplitudes, target/current residuals, phase policy, relaxation, and normalization version.
• Restart continuation matches uninterrupted evolution within deterministic numerical tolerance.
• Near-zero current, nonfinite response, and excessive scale changes invoke documented guarded behavior without corrupting accepted state.
• Single-step runs, parameter scans, and full time evolution use one shared normalization implementation.
• A multi-step test demonstrates profile update, response refresh, shielding rescaling, rejection rollback, and restart.

Blocked by

• [QL-Balance] Normalize one periodic mode to the target shielding current #292
• [QL-Balance] Run multiple periodic KIM modes with profile feedback #293