chore(deps): update dependency posthog-js to v1.262.0 (#717)

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 | minor | [`1.261.8` ->
`1.262.0`](https://renovatebot.com/diffs/npm/posthog-js/1.261.8/1.262.0)
| [![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>

###
[`v1.262.0`](https://redirect.github.com/PostHog/posthog-js/releases/tag/posthog-js%401.262.0)

[Compare
Source](https://redirect.github.com/PostHog/posthog-js/compare/posthog-js@1.261.8...posthog-js@1.262.0)

#### 1.262.0

##### Minor Changes

-
[#&#8203;2296](https://redirect.github.com/PostHog/posthog-js/pull/2296)
[`f9fe3ba`](https://redirect.github.com/PostHog/posthog-js/commit/f9fe3ba56c96ae3b6c0716ec24de68123422643f)
Thanks [@&#8203;pauldambra](https://redirect.github.com/pauldambra)! -
feat: switch replay default to lazy loading

</details>

---

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bun.lock

@@ -39,7 +39,7 @@
     "gray-matter": "4.0.3",
     "lucide-react": "0.543.0",
     "next": "15.5.2",
-    "posthog-js": "1.261.8",
+    "posthog-js": "1.262.0",
     "posthog-node": "5.8.2",
     "prettier": "3.6.2",
     "react": "19.1.1",