refactor(api): centralize password reset URL builder

[sergey3bv]

Summary

• Added centralized password reset link builder;
• Added focused unit coverage.

Avoid naming corporate partners, customers, or other sensitive external brands in this PR title or body. Use generic descriptors unless a maintainer explicitly approves the public reference.

Motivation

• A follow-up for feat(auth): include email in password-reset URL for password-manager pairing #92

Related Issue

• Closes refactor(auth): centralize and test password reset URL construction #138

Testing

• cargo test --workspace --verbose
• cargo clippy --workspace --all-targets --all-features -- -D warnings -A deprecated
• cargo fmt --all -- --check
• Manual verification completed

Visuals

• UI/web change with screenshots/video attached
• No visual change
• Visuals and text avoid sensitive external brand or partner names unless explicitly approved