Atmega328U and bootloader/uploading sketches

OK! This is actually good progress even though still not success.

The problem is that the tutorial is for the ATmega328P, but you have the ATmega328. Despite being very similar chips, they do have different signatures.

The easiest way to add support to the Arduino IDE for the ATmega328 is by using MiniCore. Please do this:
Install MiniCore by following these instructions: GitHub - MCUdude/MiniCore: Arduino hardware package for ATmega8, ATmega48, ATmega88, ATmega168, ATmega328 and ATmega328PB (NOTE: stop when you get to the part that says "Manual Installation", you only need to do the Boards Manager installation).
Select Tools > Board > ATmega328 from the menu.
Select Tools > Variant > 328 / 328A from the menu.
Select Tools > Programmer > Arduino as ISP (MiniCore) from the menu.
Click Tools > Burn Bootloader.


I'll also note that your breadboard layout is very far from being ideal. It might work, it might not work, it might work sometimes but not reliably.

You are missing the 0.1 uF capacitors on the ATmega328's power inputs. You can see here how those should be added:

The wires for your crystal circuit are way too long. You can see how it should be done here:

I would even recommend cutting the leads on the capacitors down to the necessary length.