I want to record audio WITH. an effect in Logic Pro

Two different things, printing FX on input and printing the sends/busses. To record - print - the FX on input you can go into the environment (mixer layer) and create an input channel strip, put your FX on there.

Or you can change the output of the channel to a bus and make a new audio track with that bus as the input. You would also use this technique for recording the sends from that track. The output of the AUX track where you put the send FX would be output to a bus that is used as the input of another audio track.

There's also the "Input" channel strip option.

Create an Input channel strip in your Mixer Environment, any effects you use as an insert or on a bus will be printed directly to the audio file when recording. This is different than printing and "effects" only track.

This is from L9 but the environment hasn't changed.

https://www.youtube.com/watch?v=705gAwqA8dk