Hi @Al , welcome to Microsoft Q&A forum.
I am able to repro the issue with multiple versions of SSMS. As per the error message 'SearchPropertyList' is not supported in Azure SQL Database but if we try to create it using TSQL it works.(CREATE SEARCH PROPERTY LIST)
CREATE SEARCH PROPERTY LIST DocumentPropertyList;
GO
USE yourdatabase;
ALTER FULLTEXT INDEX ON schemaname.tableName
SET SEARCH PROPERTY LIST DocumentPropertyList
WITH NO POPULATION;
GO
This looks an integration issue between SSMS and Azure SQL Database Full-Text Index. If you check the storage as mentioned in the below screenshot, it is missing the 'Search Property Lists' option, which I think is causing issue while rendering the properties GUI through SSMS.
Now as a workaround, we can use TSQL to check the properties as mentioned in below article:
View the properties of a full-text index
Please let us know if this helps or we can discuss further.
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