Thank you to @Crossroads :
"The limit is 200 mA Absolute Maximum per VCC & Gnd pin, then the current limit per port and per pin.
'328P in a DIP package has 1 VCC pin, thus 200mA limit.
'328P in a surface mount package, thus a 400mA limit.
The Notes in Section 29 show the limits per port, totalling 300mA:
ATmega48A/PA/88A/PA/168A/PA/328/P [DATASHEET] 304
8271G–AVR–02/2013
Notes: 1. “Max” means the highest value where the pin is guaranteed to be read as low
2. “Min.” means the lowest value where the pin is guaranteed to be read as high
3. Although each I/O port can source more than the test conditions (20mA at VCC = 5V, 10mA at VCC = 3V) under steady stateconditions (non-transient), the following must be observed:
ATmega48A/PA/88A/PA/168A/PA/328/P:
1] The sum of all IOH, for ports C0 - C5, D0- D4, ADC7, RESET should not exceed 150mA.
2] The sum of all IOH, for ports B0 - B5, D5 - D7, ADC6, XTAL1, XTAL2 should not exceed 150mA.
If IIOH exceeds the test condition, VOH may exceed the related specification. Pins are not guaranteed to source currgeater than the listed test condition.
4. Although each I/O port can sink more than the test conditions (20mA at VCC = 5V, 10mA at VCC = 3V)under steady state conditions (non-transient), the following must be observed:
ATmega48A/PA/88A/PA/168A/PA/328/P:
1] The sum of all IOL, for ports C0 - C5, ADC7, ADC6 should not exceed 100mA.
2] The sum of all IOL, for ports B0 - B5, D5 - D7, XTAL1, XTAL2 should not exceed 100mA.
3] The sum of all IOL, for ports D0 - D4, RESET should not exceed 100mA."
If IOL exceeds the test condition, VOL may exceed the related specification. Pins are not guaranteed to sink current greater
than the listed test condition.hl