How to read a fileGDB with multiple feature classes, reproject to GDA2020 Lat/Long using the ESRIReprojector, and write to an identically named fileGDB in a different folder?

That guide is for handling multiple FGDBs.

If the solution is just for a Single FGDB to a single FGDB, then it is much simpler. See the Guides for setting up a Dynamic Feature Reader and Feature Writer.

Please can you post a link?

I have searched but cannot find it

See here for overall Guide/Discussion

https://community.safe.com/s/article/dynamic-workflow-tutorial-introduction

The particular example workflow you probably want on this page is here. It even uses the same Reprojector Transformer required

Dynamic Workflows: Destination Schema as a Mirror Image of the Source Dataset

Note, however: Personal preference, but I generally prefer to setup my Dynamic Read/Write alternatively with a Dynamic FeatureReader and Dynamic FeatureWriter. It takes a little less effort to author it in the Workspace and automatically produces the separate Schema features as a built-in output to the FeatureReader.

For dynamic reading/writing using FeatureReader+FeatureWriter, just need to route the "Schema" output port of the FeatureReader to the Generic input of a FeatureWriter set to Dynamic Writer mode. As long as a Schema Feature is always the first feature input to the FeatureWriter for every Feature Class to be created (and it almost always is in most dynamic workflows), then FeatureWriter will read this first-in Schema feature as a "special" Feature that isn't itself a row to be written into an output Feature Class/Table but rather is the Schema feature that is processed to determine the name of Feature Class/Table to create, and its fields, so that all the following features are written against the Feature Class/Table created by that single, first-in Schema Feature.

A related question; I am using the ESRI Reprojector to do the task of reprojection.

However, the ESRI Reprojector requires me to explicitly set the Source coordinate system. Since some feature classes are lat/long and some features classes are easting/northing I am using a coordinatesystemextractor to extract a feature's coordinate system to an attribute and then filtering on that attribute.

Is there an alternative filter that will filter directly on a features coordinate system?