I have tried to search, but I can't seem to find an implementation of Banker's Rounding Mode in Postgresql. I found this thread in which there was an effort to create an implementation in T-SQL https://www.sqlservercentral.com/Forums/Topic246556-8-1.aspx.
For example, Andrew Vasylevskyy nicely gives some examples
Examples of banker's rounding (results of Math.Round in .NET):
Math.Round(3.454,2) -> 3.45
Math.Round(3.455,2) -> 3.46
Math.Round(3.445,2) -> 3.44
Math.Round(3.456,2) -> 3.46
Based on this thread PostgreSQL round(v numeric, s int) it appears that there is not a way to configure the default round() function to use a specific mode and that it does not use Banker's Rounding Mode. I do see there is a round_half_even or a round_half_odd but it is my understanding it is not the same as Banker's rounding.
Has anyone created a function that does this or is there an extension out there that can be added to do this?