feat: add C implementation for stats/base/dists/t/quantile

[Planeshifter]

Progresses stdlib-js/metr-issue-tracker#1236.

Description

What is the purpose of this pull request?

This pull request:

• adds a C implementation for @stdlib/stats/base/dists/t/quantile

The implementation uses kernel-betaincinv directly, preserving both the inverse value and its complement via out-pointers to maintain numerical accuracy in extreme tails (avoids recomputing the complement via subtraction).

Related Issues

Does this pull request have any related issues?

This pull request:

• is stacked on top of feat: add C implementation for stats/base/dists/f/quantile #15410

Questions

Any questions for reviewers of this pull request?

No.

Other

Any other information relevant to this pull request? This may include screenshots, references, and/or implementation notes.

No.

Checklist

Please ensure the following tasks are completed before submitting this pull request.

• Read, understood, and followed the contributing guidelines.

AI Assistance

When authoring the changes proposed in this PR, did you use any kind of AI assistance?

• Yes
• No

If you answered "yes" above, how did you use AI assistance?

• Code generation (e.g., when writing an implementation or fixing a bug)
• Test/benchmark generation
• Documentation (including examples)
• Research and understanding

Disclosure

If you answered "yes" to using AI assistance, please provide a short disclosure indicating how you used AI assistance. This helps reviewers determine how much scrutiny to apply when reviewing your contribution. Example disclosures: "This PR was written primarily by Claude Code." or "I consulted ChatGPT to understand the codebase, but the proposed changes were fully authored manually by myself.".

This PR was written primarily by Claude Code under my direction.

---

@stdlib-js/reviewers

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
stats/base/dists/t/quantile	$\\color{red}297/300$ $\\color{green}+0.00\\%$	$\\color{green}24/24$ $\\color{green}+0.00\\%$	$\\color{red}3/4$ $\\color{green}+0.00\\%$	$\\color{red}297/300$ $\\color{green}+0.00\\%$

The above coverage report was generated for the changes in this PR.