[Broken Website] LogRocket.com's replay does not work when Dark Reader is on.

### Prerequisites

- [X] I [searched for any existing report](https://github.com/darkreader/darkreader/issues?q=is%3Aissue) about this website issue to avoid opening a duplicate.
- [X] I can reproduce this website issue in a new, unmodified web browser profile with Dark Reader installed as the only extension.

### Website Issue Description

The playback does not navigate between pages (only tested on a React site). All the user input is shown on the first page only.

### Website Address

https://app.logrocket.com

### Steps To Reproduce

1. Set up LogRocket on a website.
2. Navigate to LogRocket's website
3. Navigate to Sessions
4. Play back a session

### Screenshots

_No response_

### Operating System

Windows 11

### Web Browser name and version

Firefox 117.0

### Dark Reader version

4.9.65

### Additional Context

_No response_