Fix eig_occ.txt lifecycle

[MoseyQAQ]

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

Fix #7751

Unit Tests and/or Case Tests for my changes

• PASS: OMP_NUM_THREADS=1 ctest --test-dir build -V -R '^MODULE_IO_write_eig_occ_test$'
• PASS: python3 -m unittest abacuslite.io.latestio.TestLatestIO (10 tests)
• NOTE: An ad hoc 2-rank run hits the existing fixed 299 plane wave assertion; MPI reduction produces 598. This is unrelated to this change.

What's changed?

• Reset eig_occ.txt for new calculations and append later ionic steps or MD restarts, independently of out_app_flag.
• Prevent abacuslite.read_abacus_out() from deleting eig_occ.txt.
• Extend focused C++ and Python tests.
• No documentation update required: this change does not modify INPUT definitions or the output file format.

Governance Notes

• INPUT/docs changes:
• Core module impact:
• Exceptions requested:

[mohanchen]

LGTM, thanks for your contribution!