Changes related to the rebranding

[meili-bot]

This PR is auto-generated.

Following the central issue: https://github.com/meilisearch/integration-guides/issues/168

• [X] Change the name MeiliSearch to meilisearch in README.
• [ ] ⚠️ Ensure the bot did not update part you don’t want it to update, especially in the code examples in the Getting started.
• [ ] Please, ensure there is no other "MeiliSearch". For example, in the comments or in the tests name. For the exposed variable names (like MeiliSearchClient) don't change anything since it would be breaking. We'll make a decision about it later.
• [ ] Put the new logo on the README you can find here if needed.

[bidoubiwa]

The PR is not up to date with the naming choices. Because the PR's are generated, it needs to be manually closed.