string or binary data would be truncated in table '******', column '******'. Truncated value: '******'
It looks like this table was defined with dynamic data masking, and the user that the application uses to access the database doesn't have permission to view masked data (which is good!).
This is why the behavior differs between the application and SSMS: I expect you're using a higher-privileged user when running the query from SSMS
Here's a demo:
CREATE TABLE dbo.Test
(
    Id int IDENTITY PRIMARY KEY,
    Filler varchar(100) MASKED WITH (FUNCTION = 'partial(1,&quot;XXXXXXX&quot;,0)') NULL
);
GO

CREATE USER TestUser WITHOUT LOGIN;  
GRANT SELECT ON dbo.Test TO TestUser;  
GRANT INSERT ON dbo.Test TO TestUser;
GO

EXECUTE AS USER = 'TestUser';
INSERT dbo.Test 
    (Filler)
VALUES
    (REPLICATE(N'A', 101)); 
REVERT;

The result of which is:
Msg 2628, Level 16, State 1, Line 12
String or binary data would be truncated in table '******', column '******'. Truncated value: '******'.

To get the full message in the application, you'll need to grant the user the UNMASK permission:
GRANT UNMASK TO TestUser;

Running the INSERT code again results in the full error text:
Msg 2628, Level 16, State 1, Line 14
String or binary data would be truncated in table 'tempdb.dbo.Test', column 'Filler'. Truncated value: 'AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA'.


When using Azure SQL Database, Dynamic Data Masking can also be configured in the Azure Portal user interface.  You may want to check there (although as far as I can tell, masks set up this way still update the sys.columns metadata):

I would also check if there are other databases that are part of the same logical SQL Server instance in Azure - maybe there are some kind of strange, cross-database queries going on.