Hi Adam,
ABAP in Eclipse is a development environment for ABAP. It has nothing to do with the HANA database or sidecar scenarios. You can use ABAP in Eclipse on every database. It is used to edit ABAP source code.
Every source code editable in the SAP GUI can also be written in ABAP in Eclipse and vice versa. Because not ABAP in Eclipse runs the source code, but the SAP Netweaver AS ABAP. So you can access your side car from the SAP GUI or from ABAP in Eclipse. This doesn't matter at all.
If you want, you could even write your ABAP source code in a command line editor like VI (or say, notepad) and upload it to the Netweaver via a command line RFC program. I even know guys who did this before.
Inside your ABAP program, which you wrote with an editor of your choice, you can access the side car by many methods. You mentioned two of them. Another one is the CALL DATABASE PROCEDURE ABAP command, which can call database procedures via a CONNECTION parameter much better than ADBC.
Best regards,
Kilian.