Your 328 symbol is incorrect:
3, 5, 21 are Gnd
4, 6 are VCC
18 is AVCC
20 is Aref
So you are missing some connections. The datasheet says all connections to power & gnd must be made.
1K from Reset to VCC is a pretty strong pullup, that might be too much for other devices to pull Reset low. 10K is standard.
47pF will impact the crystal operation, replace with 22pF.
If you are replacing the '328, replace with a '328P.
Your ICSP header is not standard. That could impact whatever programmer you are connecting. You might need an adapter cable:
MISO 1 6 VCC
SCK 2 5 MOSI
Reset 3 4 GND
Aref should be a cap to Gnd. 47uF is too big 0.1uF is standard to eliminate high frequency noise.
If the chip is burning up, that suggests something is miswired.
Device signature of 0x00s also says the chip is not communicating.
Signature bytes:
ATmega328 0x1E 0x95 0x14
ATmega328P 0x1E 0x95 0x0F
Output is showing
Arduino: 1.8.13 (Mac OS X), Board: "Arduino Uno"
AVR Part : ATmega328P
File boards.txt in the /Arduino/hardware/arduino/avr path has
uno.build.mcu=atmega328p
uno.build.f_cpu=16000000L
uno.build.board=AVR_UNO
so you may need to change that to recognize the 328 vs 328P.
Or just get 328P chip, save a lot of headache all around.
Spend the extra 0.14 and save yourself a lot of headache.