Hi Anishma,
Regarding the language detection pricing details, you can refer the similar thread so that you can get some idea.
https://learn.microsoft.com/en-us/answers/questions/1594798/azure-language-detection-api-pricing
Using the detection API separately, followed by the translation API, could potentially be more cost-effective than relying on the translation API with auto-detection. The detection API is free to some extent, while the auto-detection feature in the translation API incurs charges. However, it's important to note that the detection API may not be completely free, so you should consider the specific usage limits and pricing details for both services to determine the most cost-effective approach for your needs.
I'm glad to hear that my response was helpful to you. And thanks for sharing the information, which might be beneficial to other community members reading this thread as solution. Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others ", so I'll convert the previous response to an answer in case you'd like to accept the answer. This will help other users who may have a similar query find the solution more easily. If you have any further questions or concerns, please don't hesitate to ask. We're always here to help.