In Strategy Developer, the user could see Insert-> Transformations on a report for a metric, however, it’s not able to see it on Strategy Web for the same metric inside the same report.

There are two separate symptoms on the Strategy Web as follows.
The user cannot even see Transformation’s previous level Insert Metric option on the Strategy Web.

According to the design of the Transformation, the derived metric will be created to display the transformation, so Web users need to be granted the Client-Reporter > Web create Derived Metrics and Derived Attributes privilege to see the Insert Metric->Transformation option.
Assign the Client-Reporter > Web create Derived Metrics and Derived Attributes privilege to the user.
The user is able to see the previous level Insert Metric option on the Strategy Web, but there's no Transformation option.

The transformation option is related to the Schema Objects\Transformation folder, which contains the transformations that could be applied to the metric. Thus, the user should have view access to the Transformation folder.
Assign the View permission to the user to access the Transformation folder in Developer.

If the issue persists, please double-check whether ALL users including the Administrator user encounter the same issue. If so, please check whether there’re any web customizations or SDK which might disable specific options. You could try to deploy an OOTB web war file to confirm that.