The custom filters are in the database as XML stored as binary, so they have to be converted to be read. This will do it:
select CAST(CAST(FilterData AS VARBINARY(MAX)) AS XML), * from [BFEnterprise].[dbo].[NAMEDFILTERS]
Thanks to @Aram for this.
They don’t use session relevance, at least not for the filter definition.
Related: Add ability for console filters to show only items with default actions