fix: resolve all pre-commit type errors and add missing route files

[promisszn]

Description

Closes #729
Closes #730
Closes #737
Closes #741

Changes proposed

What were you told to do?

Implement four new utility API endpoints inside app/api/routes-f/:

• feat(routes-f): gcd and lcm calculator for multiple numbers #729 – GCD and LCM calculator for multiple numbers
• feat(routes-f): quadratic equation solver #730 – Quadratic equation solver (real and complex roots)
• feat(routes-f): http cookie parser and builder #737 – HTTP Cookie parser and builder
• feat(routes-f): character statistics by unicode category #741 – Character statistics by Unicode category

What did you do?

GCD/LCM Calculator (app/api/routes-f/gcd-lcm/) — #729

• Added route.ts — POST /api/routes-f/gcd-lcm accepts { numbers: number[], operation?: "both" | "gcd" | "lcm" }, returns { gcd?, lcm?, n_count }
• Added _lib/helpers.ts — Euclidean GCD, LCM via |a*b|/gcd(a,b), BigInt intermediate arithmetic to prevent overflow, validates positive integers with a 100-element cap
• Added _lib/types.ts — GcdLcmInput, GcdLcmResponse, Operation types
• Added __tests__/gcd-lcm.test.ts — covers known pairs, multiple numbers, primes, single element, and validation errors

Quadratic Solver (app/api/routes-f/quadratic/) — #730

• Added route.ts — POST /api/routes-f/quadratic accepts { a, b, c }, returns { roots, discriminant, vertex, axis_of_symmetry, has_complex_roots }
• Added _lib/helpers.ts — solves ax² + bx + c = 0 for real distinct, repeated, and complex roots; rejects a = 0; rounds to 6 decimal places
• Added _lib/types.ts — Root, Vertex, QuadraticResponse types
• Added __tests__/quadratic.test.ts — covers all root types, vertex/axis calculation, and a = 0 rejection

Cookie Parser & Builder (app/api/routes-f/cookie-parse/) — #737

• Added route.ts — POST /api/routes-f/cookie-parse accepts { mode: "parse" | "build", input }, returns a parsed cookie object or a Set-Cookie header string
• Added _lib/helpers.ts — parses Cookie/Set-Cookie headers into structured objects with all attributes (expires, max_age, domain, path, secure, http_only, same_site); builds Set-Cookie strings; URL-decodes values; validates same_site enum
• Added _lib/types.ts — CookieAttributes, ParsedCookies types
• Added __tests__/cookie-parse.test.ts — covers parse with all attributes, build round-trip, multiple cookies, and invalid input rejection

Character Statistics (app/api/routes-f/char-stats/) — #741

• Added route.ts — POST /api/routes-f/char-stats accepts { text }, returns { total, letters, digits, whitespace, punctuation, symbols, emoji, other, by_script }
• Added _lib/helpers.ts — Unicode property regexes (/\p{L}/u etc.), multi-codepoint ZWJ emoji handling via Intl.Segmenter, script detection for Latin/Cyrillic/CJK/Arabic, 1 MB input cap
• Added _lib/types.ts — CharStatsResponse, ScriptBreakdown types
• Added __tests__/char-stats.test.ts — covers ASCII, mixed scripts, emoji sequences, and size limit enforcement

Check List (Check all the applicable boxes)

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• The title and description of the PR is clear and explains the approach.
• I am making a pull request against the main branch (left side).
• My commit messages styles matches our requested structure.
• My code additions will fail neither code linting checks nor unit test.
• I am only making changes to files I was requested to.

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