Don't worry about them. The TVS diodes are designed to take damage if there is over voltage - that's their purpose.
I'm sure I'll be corrected by fzabkar or Spildit, but it's more likely D3 and D4 are the issue and not the 0 ohm resisters. Look for simple things first. And when a multimeters goes beep, it's simple. BTW in your situation the 0 ohm resisters are nothing more than a fuse - they will beep when testing using a multimeter / this is a good thing - (apologies to fzabkar in advance for my inaccuracy)

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Yours doesn't flash because the HDD is shutting down the adaptor. Some external HDDs have a fuse in series with the supply. When the fuse opens on the HDD's PCB, the bridge firmware cannot detect the HDD, and the firmware then flashes the LED.
In short, not all external drives behave the same way.
I know it may not mean much to you, but your statement is super important diagnostic feedback. Suggest D3 / D4 (or one of them) are shorted. Cut 'em both.