Update dependency mongoose to v8.16.1 (#273)

This PR contains the following updates:

| Package | Change | Age | Adoption | Passing | Confidence |
|---|---|---|---|---|---|
| [mongoose](https://mongoosejs.com)
([source](https://redirect.github.com/Automattic/mongoose)) | [`8.16.0`
-> `8.16.1`](https://renovatebot.com/diffs/npm/mongoose/8.16.0/8.16.1) |
[![age](https://developer.mend.io/api/mc/badges/age/npm/mongoose/8.16.1?slim=true)](https://docs.renovatebot.com/merge-confidence/)
|
[![adoption](https://developer.mend.io/api/mc/badges/adoption/npm/mongoose/8.16.1?slim=true)](https://docs.renovatebot.com/merge-confidence/)
|
[![passing](https://developer.mend.io/api/mc/badges/compatibility/npm/mongoose/8.16.0/8.16.1?slim=true)](https://docs.renovatebot.com/merge-confidence/)
|
[![confidence](https://developer.mend.io/api/mc/badges/confidence/npm/mongoose/8.16.0/8.16.1?slim=true)](https://docs.renovatebot.com/merge-confidence/)
|

---

### Release Notes

<details>
<summary>Automattic/mongoose (mongoose)</summary>

###
[`v8.16.1`](https://redirect.github.com/Automattic/mongoose/blob/HEAD/CHANGELOG.md#8161--2025-06-26)

[Compare
Source](https://redirect.github.com/Automattic/mongoose/compare/8.16.0...8.16.1)

\===================

- fix(document): avoid setting \_skipMarkModified when setting nested
path with merge option
[#&#8203;15484](https://redirect.github.com/Automattic/mongoose/issues/15484)
[#&#8203;11913](https://redirect.github.com/Automattic/mongoose/issues/11913)
- fix(model): make sure post save error handler gets doc as param on
VersionError
[#&#8203;15483](https://redirect.github.com/Automattic/mongoose/issues/15483)
[#&#8203;15480](https://redirect.github.com/Automattic/mongoose/issues/15480)
- fix: consistent $conditionalHandlers setup between schematypes
[#&#8203;15490](https://redirect.github.com/Automattic/mongoose/issues/15490)
- docs(compatibility): note that mongodb 4.0 is not supported anymore
since 8.16.0
[#&#8203;15487](https://redirect.github.com/Automattic/mongoose/issues/15487)
[hasezoey](https://redirect.github.com/hasezoey)
- docs: remove unnecessary --save flag from npm install instruction
[#&#8203;15486](https://redirect.github.com/Automattic/mongoose/issues/15486)
[Thahirgeek](https://redirect.github.com/Thahirgeek)

</details>

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