Fix: Replace React badges with new versions (#4163)

## Because
- The current ones use the wrong color


## This PR
- Replaces them with new amazing versions by @ManonLef 


## Issue
Closes: #4088 

## Additional Information
<!-- Any other information about this PR, such as a link to a Discord
discussion. -->


## Pull Request Requirements
<!-- Replace the whitespace between the square brackets with an 'x',
e.g. [x]. After you create the PR, they will become checkboxes that you
can click on. -->
- [x] I have thoroughly read and understand [The Odin Project
Contributing
Guide](https://github.com/TheOdinProject/theodinproject/blob/main/CONTRIBUTING.md)
- [x] The title of this PR follows the `keyword: brief description of
change` format, using one of the following keywords:
    - `Feature` - adds new or amends existing user-facing behavior
- `Chore` - changes that have no user-facing value, refactors,
dependency bumps, etc
    - `Fix` - bug fixes
-   [x] The `Because` section summarizes the reason for this PR
- [x] The `This PR` section has a bullet point list describing the
changes in this PR
- [x] I have verified all tests and linters pass after making these
changes.
- [x] If this PR addresses an open issue, it is linked in the `Issue`
section