Refactor: structured INPUT parameter availability (Phase 1)

[Stardust0831]

Reminder

• I have read AGENTS.md and docs/developers_guide/agent_governance.md.
• I have linked an issue or explained why this PR does not need one.
• I have added adequate unit tests and/or case tests, or explained why not.
• I have listed the exact verification commands run and their results.
• I have described user-visible behavior changes, including INPUT parameter changes.
• I have explained core-module impact for ESolver, HSolver, ElecState, Hamilt, Operator, Psi, or other source/ changes.
• I have requested any needed governance exception below.

Linked Issue

Ref #7719 — normalize INPUT availability into a machine-readable form and align it with parameter validation.

Unit Tests and/or Case Tests for my changes

• Commands run:
  • python3 tools/03_code_analysis/test_availability_parser.py — 17 tests, all pass (incl. precedence for and/or/parentheses, contains semantics, and a validation that every non-empty availability in docs/parameters.yaml parses as Expression).
  • New C++ parser unit test source/source_io/test_serial/availability_test.cpp wired into the test build (BUILD_TESTING=ON); covers leaf/in-set/contains/and-or nesting/round-trip/empty/string-end edge inputs.
  • Remote CPU build + abacus --generate-parameters-yaml — COMPLETED; regenerated docs/parameters.yaml and input-main.md (generated output byte-consistent with the checked-in docs).
• Result summary: docs/parameters.yaml has 526 params / 216 non-empty availability, all concrete boolean Expression (0 Label / 0 Unstructured).
• Checks not run, with reason: full runtime/MPI test suite not run — this change is metadata-only (availability strings + help export); no numerical or code-path behavior change.

What's changed?

Make the Input_Item availability field a single-source, machine-evaluable boolean condition so the INPUT docs, validation and tooling can consume and evaluate it instead of re-parsing free text or bare tags.

• C++ data model: new dependency-free module source/source_io/module_parameter/availability.{h,cpp} (wired into CMake) with AvailabilityCondition / AvailabilityExpr and parse_availability() (operators ==/!=/>/>=/</<=/in/contains, combinators and/or/,, (...) grouping). Input_Item keeps the canonical availability string plus availability_expr (parsed tree) and a set_availability() helper keeping both in sync (single source of truth).
• Migration: all 217 non-empty availability registrations rewritten to canonical boolean syntax. Former bare "label"-style tags (OFDFT, Numerical atomic orbital basis, ...) are now concrete conditions over existing parameters (esolver_type==ofdft, basis_type==lcao, calculation==gen_bessel, dft_plus_u==1, ...). Vector parameters use contains (e.g. td_ttype contains 2) to preserve containment semantics.
• Export: --generate-parameters-yaml now emits the canonical availability string (empty string = always available) and nothing else, keeping the YAML lean; the structured parse tree stays in C++ for a future validation/error layer.
• Docs: regenerated docs/parameters.yaml and input-main.md.

Manual fidelity: rewrites preserve the manual's original meaning. Where the manual states a gate the code does not enforce via an INPUT boolean, it is called out in Governance Notes.

Governance Notes

• INPUT/docs changes: docs/parameters.yaml and docs/advanced/input_files/input-main.md regenerated from the new binary (per AGENTS.md). Full old→new mapping was reviewed locally.
• Core module impact: source/source_io/module_parameter/input_item.h gains an availability_expr member and the new availability module; metadata-only, no runtime/numerical behavior change.
• Exceptions requested:
  • Header dependency review: input_item.h includes availability.h because Input_Item holds AvailabilityExpr by value (a forward declaration is not possible); availability.h includes <string>/<vector> for its members (std::string, std::vector). Required includes, not reducible to forward declarations.
• Manual-vs-code discrepancies documented (not acting on them in this PR):
  • mixing_dmr: manual >= 0.0 (always true) kept as mixing_restart>=0; esolver checks > 0 — likely loose manual wording.
  • mixing_tau: "Only relevant for meta-GGA" is a note decided at runtime (XC_Functional::get_ked_flag), not an INPUT gate; availability empty, note kept in description.
  • fixed_ibrav: encoded as relax_method in [cg 2] and latname != none (both manual clauses; the latter also enforced by check_value).