docs: add style-guide rule against "whose" for non-person antecedents (#27866)

## What

Adds a Word choice entry to the docs style guide, **"Whose for people,
not things"**. It restricts "whose" to people and points writers to
"with", "where", or "that has" for inanimate objects and abstract
concepts, since "whose" implies personhood.

## Where

`docs/.style/style-guide/word-choice.md`, inserted right after **Phrasal
verbs and their noun forms**, the closest existing grammar/usage rule.
Formatting matches the surrounding entries: sentence-case H2, a
two-sentence rationale (one sentence per line), `**Do**` / `**Don't**`
blockquotes, and a documentation-only enforcement note.

## Rule

> "Whose" is the possessive of "who", so it implies the antecedent is a
person.
> When the antecedent is an inanimate object or an abstract concept,
prefer "with", "where", or "that has".

Example:

- Don't: A chat whose gateway records have been pruned reports no cost.
- Do: A chat with pruned gateway records reports no cost.

## Notes

- Docs-only change (Markdown under `docs/`, no CI or build config), so
it's out of scope for `/coder-agents-review`; the doc-check agent covers
docs-only PRs.
- The style-guide subpages are Vale-exempt, so no Vale rule ships with
this. The enforcement note reads "Documentation-only. No Vale rule.",
matching the other documentation-only entries.

Linear:
[DOCS-612](https://linear.app/codercom/issue/DOCS-612/style-guide-avoid-whose-for-non-person-antecedents)

> This PR was created with AI assistance (Coder Agents).

docs/.style/style-guide/word-choice.md

@@ -150,6 +150,30 @@ Treat them consistently across the docs.
 
 *Enforced by `Coder.PhrasalVerbs` (planned).*
 
+## Whose for people, not things
+
+"Whose" is the possessive of "who", so it implies the antecedent is a person.
+When the antecedent is an inanimate object or an abstract concept, prefer "with", "where", or "that has".
+
+**Do**:
+
+> A chat with pruned gateway records reports no cost.
+>
+> A template that has conflicting variables fails validation.
+>
+> A region where every proxy is unhealthy drops workspace connections.
+
+**Don't**:
+
+> A chat whose gateway records have been pruned reports no cost.
+>
+> A template whose variables conflict fails validation.
+>
+> A region whose proxies are all unhealthy drops workspace connections.
+
+*Documentation-only.
+No Vale rule.*
+
 ## Refer to, check out, visit, not see
 
 When the prose points the reader at another page, section, or external resource, choose the verb that matches the register: