docs: fix typos discovered by codespell (#2534)

## Description

<!-- A summary of what this pull request achieves and a rough list of
changes. -->

% `codespell
--ignore-words-list=ans,crate,inout,ratatui,ser,stayin,swarmin,worl`
* https://github.com/codespell-project/codespell

## Breaking Changes

<!-- Optional, if there are any breaking changes document them,
including how to migrate older code. -->

## Notes & open questions

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-->

## Change checklist

- [x] Self-review.
- [ ] Documentation updates following the [style
guide](https://rust-lang.github.io/rfcs/1574-more-api-documentation-conventions.html#appendix-a-full-conventions-text),
if relevant.
- [ ] Tests if relevant.
- [ ] All breaking changes documented.

src/engine.rs

@@ -393,7 +393,7 @@ pub struct DefaultAuthor {
 impl DefaultAuthor {
     /// Load the default author from storage.
     ///
-    /// If the storage is empty creates a new author and perists it.
+    /// If the storage is empty creates a new author and persists it.
     pub async fn load(storage: DefaultAuthorStorage, docs_store: &SyncHandle) -> Result<Self> {
         let value = storage.load(docs_store).await?;
         Ok(Self {