chore(deps): update dependency posthog-js to v1.256.2 (#579)

This PR contains the following updates:

| Package | Type | Update | Change | OpenSSF |
|---|---|---|---|---|
| [posthog-js](https://posthog.com/docs/libraries/js)
([source](https://redirect.github.com/PostHog/posthog-js)) |
dependencies | patch | [`1.256.0` ->
`1.256.2`](https://renovatebot.com/diffs/npm/posthog-js/1.256.0/1.256.2)
| [![OpenSSF
Scorecard](https://api.securityscorecards.dev/projects/github.com/PostHog/posthog-js/badge)](https://securityscorecards.dev/viewer/?uri=github.com/PostHog/posthog-js)
|

---

### Release Notes

<details>
<summary>PostHog/posthog-js (posthog-js)</summary>

###
[`v1.256.2`](https://redirect.github.com/PostHog/posthog-js/releases/tag/v1.256.2):
1.256.2

[Compare
Source](https://redirect.github.com/PostHog/posthog-js/compare/v1.256.1...v1.256.2)

##### 1.256.2 - 2025-07-04

- fix: Fix backwards compatibility
([#&#8203;2074](https://redirect.github.com/PostHog/posthog-js/issues/2074))
- feat: Sdk spec gen
([#&#8203;2029](https://redirect.github.com/PostHog/posthog-js/issues/2029))
- Fix CHANGELOG.md
([#&#8203;2068](https://redirect.github.com/PostHog/posthog-js/issues/2068))

###
[`v1.256.1`](https://redirect.github.com/PostHog/posthog-js/releases/tag/v1.256.1):
1.256.1

[Compare
Source](https://redirect.github.com/PostHog/posthog-js/compare/v1.256.0...v1.256.1)

#### 1.256.1 - 2025-07-02

- fix survey input color on dark backgrounds
([#&#8203;2071](https://redirect.github.com/PostHog/posthog-js/issues/2071))

</details>

---

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## Summary by Sourcery

Update posthog-js to v1.256.2 to incorporate upstream patches and new
SDK features.

New Features:
- Pull in SDK spec generation support introduced in posthog-js v1.256.2.

Bug Fixes:
- Restore backwards compatibility in posthog-js.
- Fix survey input color on dark backgrounds.

Documentation:
- Correct CHANGELOG.md in posthog-js.

Chores:
- Bump posthog-js dependency from v1.256.0 to v1.256.2.

Signed-off-by: renovate[bot] <29139614+renovate[bot]@users.noreply.github.com>
Co-authored-by: renovate[bot] <29139614+renovate[bot]@users.noreply.github.com>

Author: renovate[bot]

bun.lock

@@ -39,7 +39,7 @@
     "gray-matter": "4.0.3",
     "lucide-react": "0.525.0",
     "next": "15.3.4",
-    "posthog-js": "1.256.0",
+    "posthog-js": "1.256.2",
     "posthog-node": "5.1.1",
     "prettier": "3.6.2",
     "react": "19.1.0",