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Thanks I will either use I2C Multiplexer or add another I2C bus in the design.

Regarding the value of shunt resistor. I did following calculation.

According to datasheet, the maximum voltage across shunt resistor is +/- 163 mV.

I have 3.6 A max running through the power cables. The supply voltage at the load is 3.3 V.

I found 39 mOhm through hole resistor having power rating 3 W tolerance +/- 5%.  I also found SMD with tolerance 1%.

The voltage across shunt resistor will be

V = I x R

V = 3.6 x 39/1000

V = 140 mV

The power dissipation across shunt resistor will be

P = V x I

P = 140/1000 * 3.6

P = 0.5 Watt

What will be the resolution of the current measurement ?

Considering 2 bit noise in 13 bit ADC.

3.6 A / 2048 = 1.75 mA

Is my calculation make sense for 11 bit ADC ?

Link to datasheet INA3221 is

[URL unfurl="true"]https://www.ti.com/lit/ds/symlink/ina3221.pdf?ts=1723033414709&ref_url=https%253A%252F%252Fwww.ti.com%252Fproduct%252FINA3221%252Fpart-details%252FINA3221AIRGVT%253Fbm-verify%253DAAQAAAAJ_____6Q9ESDlkK-ssOyIW2326HprlH3nSauvtP5Qa4R6rwWoLFMSN3alQs9zOKHsPlyc0rd0yZ2mP3bmweis1qmHoYDmPmdIw1NMdRG2I8zcOHgxqzObd3jm2slufZBZM48jCQDfocCDnbG7eAMZRMwd_MdLXkAU0zrhPDWKRYvmyyTsWFLIqG41fgQmU6yhaUFKfhEpOxCor4Rfrp_9-VmhlRitKm4vflAZhBmvRz-WqqTTVIW2S7buVUgMdaNGfsfqJYL_Fq0hEkLb1FdE46R2dGVpo23Y1hRVGF8VPcujyi2DH4D6IIDGq4e37gQOxszyinwiMTwDW1ptExkL8QVMs0gZYA[/URL]