I was having trouble connecting with Windows Authentication as well. I found that I was getting a similar error from the Gateway Status page...
Cannot create PoolableConnectionFactory (This driver is not configured for integrated authentication.
I noticed further down in the stack trace however, that the driver version Ignition was looking for did not match the latest version I downloaded (per the User Manual Guide: Connecting to Microsoft SQL Server, Scenario 2: Connect By Using Instance Name and Windows Authentication)
java.lang.UnsatisfiedLinkError: no mssql-jdbc_auth-9.4.0.x64 in java.library.path: [lib, lib\core\gateway]
I sought out, and downloaded the mssql-jdbc_auth-X.X.X.x64.dll file that matched the mssql-jdbc-9.4.0.jre11.jar file located in C:\Program Files\Inductive Automation\Ignition\user-lib\jdbc, which was 9.4.0 in my case. I put that file in the location described by the connection guide and my connection worked.
TL;DR, The connection guide should be updated to specify that the DLL file you want should match the mssql-jdbc JAR file in your user-lib/jdbc directory, instead of just "...it's recommended you use the most recent driver available for your system".
Specs: Ignition 8.1.21, Running on Windows Server 2019.