Update!
I think I made it work, thanks to you!

I can now burn the bootloader, and it gives me a long successful message.
Now I'm also able to upload sketches via the programmer!
Just one issue. When I upload the blink sketch, everything works good on the breadboard and the LED connected to pin 19 works, but when I plug it into my Arduino Uno, the sketch doesn't work and the BUILTIN led doesn't light up at all, and the reset button doesn't work. Do you know why that is?
Quick edit: Unfortunately, when I plug my recently burned ATmega328PPU chip into my Arduino Uno (elegoo), I'm unable to upload anything to the chip. This is the log when I try:
avrdude: Version 6.3-20190619
Copyright (c) 2000-2005 Brian Dean, http://www.bdmicro.com/
Copyright (c) 2007-2014 Joerg Wunsch
System wide configuration file is "C:\Program Files (x86)\Arduino\hardware\tools\avr/etc/avrdude.conf"
Using Port : COM6
Using Programmer : arduino
Overriding Baud Rate : 115200
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 1 of 10: not in sync: resp=0x7c
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 2 of 10: not in sync: resp=0x7c
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 3 of 10: not in sync: resp=0x7c
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 4 of 10: not in sync: resp=0x7c
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 5 of 10: not in sync: resp=0x7c
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 6 of 10: not in sync: resp=0x7c
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 7 of 10: not in sync: resp=0x7c
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 8 of 10: not in sync: resp=0x7c
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 9 of 10: not in sync: resp=0x7c
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 10 of 10: not in sync: resp=0x7c
avrdude done. Thank you.
Problem uploading to board. See http://www.arduino.cc/en/Guide/Troubleshooting#upload for suggestions.