Add synchronized shared-path deposition weights to OPES

[Zhang-pchao]

Summary

Add opt-in WALKERS_SHARED_BIAS for synchronized replicas belonging to one complete path. Use the mean bias plus EXTRA_BIAS as the common deposition log weight, matching a bead-average sampled bias Hamiltonian. This changes deposition weights, not forces.

Dependencies

This stacked master branch contains the kernel corrections from #1463 and input validation from #1467. The final feature commit introduces WALKERS_SHARED_BIAS and its native regression. The prerequisite fixes target v2.9 under the contribution policy; this feature targets master.

Contracts

Require WALKERS_MPI, explicit SIGMA, equal temperature and PACE, consistent flags and no EXCLUDED_REGION. Reject OPES_METAD_EXPLORE. Record the mode and bead count in histories and reject incompatible restarts. Ordinary walker behavior is retained when the option is omitted.

Walker/kernel counters are not independent complete-path sample counts. This implementation provides no accuracy or efficiency claim.

Validation

Independent current-master build with all modules; the new MPI regression checks analytic shared deposition, EXTRA_BIAS, metadata/restart compatibility and collective rejection. Full native OPES regressions passed without changed tolerances. Documentation explains force, Hamiltonian and statistical-unit conventions.

Documentation

The native current-master new-manual generator and MkDocs build completed. All changed action examples have empty stderr and are absent from the broken-example list. The full manual reports 36 failing example pages outside these actions and missing optional-module/link warnings; the full manual is not claimed to be warning-free. Inherited generic keywords are not all covered by examples.

Python/OpenMP CI follow-up

Includes the separately reviewable regression-process lifetime fix #1470, which retains the dynamically loaded kernel during Python shutdown. It preserves two-thread execution and the original numerical reference. This addresses the rt-symfunc shutdown failure observed on the debug runner.

Regression follow-up

Included the accepted rt-protein shutdown fix #1473, the rt-grid follow-up #1477, and the timestep-test initialization fix accepted in #1464. The Python configs pass three direct two-thread runs per case with byte-identical reference output; the existing build reports Python unavailable to the native runner. The timestep regression passes through the native runner with poisoned automatic-variable initialization against both v2.10 and master kernels. No reference values, tolerances or thread counts were changed. The Autoconf download failure has a separate upstream CI proposal in #1474.

Companion integration

The PIMD use case is the bead-averaged bias energy in lammps/lammps#5232 (path_integral bead_density). This PR supplies the shared OPES deposition weights; the LAMMPS PR owns integration and force/energy accounting. Its generic fixed-bias coupling does not require this OPES extension.