The best option to serve the model while optimizing cost, user experience, and ease of management is to deploy the model to Vertex AI Prediction, which is a managed service that can scale up or down according to the demand and provide low latency and high availability. Vertex AI Prediction can also handle TensorFlow models natively, without requiring any additional steps or conversions. By using batch prediction, the model can process large volumes of data efficiently and periodically, without affecting the user experience. The data can be read from Cloud Bigtable, which is a scalable and performant NoSQL database that can store user data in a flexible schema. The predictions can then be pushed to Cloud SQL, which is a fully managed relational database that can store the predictions in a structured format and enable easy querying and analysis. This option also simplifies the management of the model and the data, as it leverages the existing Google Cloud services and does not require any additional infrastructure or code.

The other options are not optimal for the following reasons:

A. Importing the model into BigQuery ML is not a good option, as it requires converting the TensorFlow model into a format that BigQuery ML can understand, which can introduce errors and reduce the performance. Moreover, BigQuery ML is not designed for serving real-time predictions, but rather for training and evaluating models using SQL queries. Reading and writing data from BigQuery and Cloud SQL can also incur additional costs and latency, as they are both relational databases that require schema definition and data transformation.

C. Embedding the model in the mobile application is not a good option, as it increases the size and complexity of the application, and requires updating the application every time the model changes. Moreover, it exposes the model to the users, which can pose security and privacy risks, as well as potential misuse or abuse. Additionally, it does not leverage the benefits of the cloud, such as scalability, reliability, and performance.

D. Embedding the model in the streaming Dataflow pipeline is not a good option, as it requires building and maintaining a custom pipeline that can handle the model inference and data processing. This can increase the development and operational costs and complexity, as well as the potential for errors and failures. Moreover, it does not take advantage of the batch prediction feature of Vertex AI Prediction, which can optimize the resource utilization and cost efficiency.