External HDD suddenly not mounting on macOS – Disk Utility sees it but won’t mount

I’m using macOS (Sonoma) and my external HDD suddenly stopped mounting.

Disk Utility still detects the drive, but:

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• it won’t mount
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• First Aid fails
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• the drive sometimes disconnects
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• data is important (photos + work files)
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I haven’t formatted anything yet.

What are the safe steps to diagnose this on macOS without risking data loss?

Are there situations where Disk Utility or Terminal commands can make things worse?