feat: add canonical PauliStringSum container

[jaimeajl]

Issue #, if available:

Closes #1256

Description of changes:

This PR adds a canonical PauliStringSum container for weighted PauliString expressions.

The implementation focuses on predictable algebraic behavior and representation fidelity across conversions:

• duplicate Pauli strings are merged deterministically;
• zero-coefficient terms are removed from the canonical representation;
• term ordering is stable;
• coefficients are restricted to real numbers;
• weighted tuple round-trips preserve algebraic meaning;
• conversions to/from Observable.Sum avoid silent semantic changes;
• unsupported operations fail explicitly.

The goal is to make weighted PauliString sums predictable across algebraic operations and representation boundaries.

Testing done:

• ruff check src/braket/quantum_information/pauli_string.py src/braket/quantum_information/__init__.py test/unit_tests/braket/quantum_information/test_pauli_string_sum.py
• ruff format --check src/braket/quantum_information/pauli_string.py src/braket/quantum_information/__init__.py test/unit_tests/braket/quantum_information/test_pauli_string_sum.py
• targeted pytest: 68 passed, 31 xfailed
• coverage for pauli_string.py: 100%
• git diff --check

AI assistance disclosure: I used AI assistance for design review and wording, then implemented, reviewed, and validated the changes locally.

Merge Checklist

General

• I have read the CONTRIBUTING doc
• I used the PR title format described in CONTRIBUTING
• I have updated any necessary documentation, including READMEs and API docs (if appropriate)

Tests

• I have added tests that prove my fix is effective or that my feature works (if appropriate)
• I have checked that my tests are not configured for a specific region or account (if appropriate)

By submitting this pull request, I confirm that my contribution is made under the terms of the Apache 2.0 license.