Document transpiler pass categories and examples

[kataro92]

Summary

Closes #3436.

This expands the qiskit.transpiler.passes API documentation with a short guide to using transpiler passes directly. It explains how passes work with PassManager, the difference between analysis and transformation passes, and how the pass categories fit into a custom transpilation workflow.

Details and comments

The current docs/apidoc/transpiler_passes.rst page renders the module docstring from qiskit.transpiler.passes, so this PR updates qiskit/transpiler/passes/__init__.py.

The new documentation:

• Adds a "Working with transpiler passes" overview.
• Explains AnalysisPass, TransformationPass, and PropertySet.
• Adds small examples using CountOps, RemoveBarriers, and InverseCancellation with PassManager.
• Adds concise descriptions for the existing pass categories, including layout, routing, basis change, optimization, scheduling, circuit analysis, synthesis, post-layout, and utility passes.

This keeps the change scoped to the transpiler-passes API page and avoids duplicating the broader preset-pass-manager overview from qiskit.transpiler.

Tests

• python -m py_compile qiskit/transpiler/passes/__init__.py
• Ran the new analysis-pass example locally.
• Ran the new transformation-pass example locally.
• git diff --check

AI/LLM disclosure

• I didn't use LLM tooling, or only used it privately.
• I used the following tool to help write this PR description: Cursor with GPT-5.5.
• I used the following tool to generate or modify code: Cursor with GPT-5.5.

I reviewed and understand the generated guidance, documentation change, examples, and test results before submitting.

[coveralls]

Coverage Report for CI Build 27249783085

Coverage decreased (-0.01%) to 87.531%

Details

• Coverage decreased (-0.01%) from the base build.
• Patch coverage: No coverable lines changed in this PR.
• 27 coverage regressions across 4 files.

Uncovered Changes

No uncovered changes found.

Coverage Regressions

27 previously-covered lines in 4 files lost coverage.

File	Lines Losing Coverage	Coverage
crates/qasm2/src/parse.rs	18	96.68%
crates/qasm2/src/lex.rs	6	92.03%
crates/circuit/src/parameter/symbol_expr.rs	2	74.17%
crates/circuit/src/parameter/parameter_expression.rs	1	91.03%

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Coverage Stats

Relevant Lines:	126602
Covered Lines:	110816
Line Coverage:	87.53%
Coverage Strength:	953029.86 hits per line

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💛 - Coveralls