Hi and Thanks for reaching out on the Redgate forums.
Regarding your query around Azure Synapse Serverless db's.
Yes, it should certainly be possible to connect to these instances and have SQL Prompt register them to provide functionality.
To test this; I connected to my Azure instance and spun up a new sample DB on a serverless compute instance and connected it to my local SMSS instance to access SQL Prompt functionality.
Have you tried connecting to an instance and are experiencing any issues in getting our tools to work?
If so please provide some further details so we can assist further
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