I personally do not like reacharound placing, so I disabled it. Now the icon doesn't show, yet blocks can still be placed on the other side of blocks.

Disabling seems to disable the icon, not the functionality 1.19.2

Edit: It might be relevant that I am on a server, so is this feature server side, forcing all clients to place blocks in that way regardless of whether they have it toggled off or not?

This can use the handshake system that was since added

Yeah, it looks like reacharound placing is handled on the server and the client just draws the icon.

There's some mechanism for allowing clients to control whether the server performs the action or not (used for Automatic Tool Restock) but it's not used for this module just yet.

This should probably be solved by making reacharound a client action it then asks the server to perform?