Can a Scrum Master also take on tasks such as writing test scripts or developing reports, especially now that GenAI tools make it easier for anyone to contribute? Traditionally, how was it viewed when Scrum Masters contributed in this way, and with GenAI potentially reducing team sizes, how might agile experts view this kind of involvement from Scrum Masters now?

I agree with other comments on keeping the focus as Scrum Master but if capacity is left then Scrum Master can definitely contribute on testing side. 

The key requirement is to have a high quality User Story with Acceptance Criteria plus any other information such as Software Requirements Specification, architecture documentation etc. LLM will use these as inputs to generate Test Cases in plain English. The test cases need to be verified for accuracy, scope... and make sure it covers positive and negative test cases. Once verified and/or updates, use the test cases again in LLM for creating the Test Script in desired language or testing framework. Or test cases can be used in Github Copilot in VS Code to create the scripts.

This is very much do-able. Infact we have created this as AI RAG application which connects with Jira, uses other referring information to create test cases and then finally test scripts. But our audience is QC team as they are overloaded.

We plan to introduce MCP server as well so that we can do the executive in AI Agent mode. It does take sometime to train the model to get the results at right level.

Hope this helps.

As long as it doesn’t distract from their core role removing impediments and supporting continuous improvement.

My recommendation is to keep the Scrum Masters focused on their primary role of driving effectiveness and continuous improvements.  If you are considering stretching the scrum master goals due to limitations on the size of the team, the most important consideration is the experience and knowledge of the Scrum master.  

Does the scrum master has the experience to take on key activities like writing test scrips or developing reports?  Even using the help of AI tools requires a good level of understanding to ensure the right outcomes or results were generated.  If there are some tasks that can be delegated to help alleviate the team's size limitations as long as the expectations are clear and there is an initial level of verification from an expert until the skills and knowledge is fully acquired by the scrum master.