Update Documentation and README.md for Client Package Refactor

[coderabbitai]

The recent refactor in the gofiber/fiber/v3/client package, which includes renaming the 'ClientNew' function to 'New', necessitates updates to the documentation and README.md to reflect these changes. This issue tracks the task of updating the documentation and README.md to ensure consistency and aid users in understanding the changes made.

PR URL: #2896
Comment URL: #2896 (comment)

The documentation and README.md for the client package are currently incomplete and need to be updated to align with the latest codebase changes. This includes updating any references to the old function name 'ClientNew' to the new name 'New', and ensuring that any examples or usage instructions are accurate and up-to-date.

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Please add more documentation and also usage example

also use this comment
#1986 (comment)

[ReneWerner87]

@coderabbitai please create a pull request with the documentation as requested in the issue description