Hi, asking Google
where does Chrome store its passwords
is the first step - two suggestions are given here, and which are relevant depends on your usage:
Anyone know how to find the password file for chrome on a hard drive? - Web Browsing/Email and Other Internet Applications
If your passwords were synched, then recovery is easy and independent of your drive.
Otherwise,
You can of course try to access that on your defective drive connected as an external drive- and hope it's intact.
However I have no idea whether transferring such a file to another instance of the browser will work. That thread indicates not.
This is a detailed Chrome question and as such might be better addressed on a Chrome forum.
I'll offer the same advice on protecting your time and your data as I've given so many times.
a. Use disk imaging routinely e.g. Macrium Reflect (free) + external storage. The you can often recover without technical help. Recommended endlessly here.
The very act of imaging requires your disk be sound. Thus if it fails to complete an image, you get an error message and are alterted.
Weekly imaging - even daily- and you see how little you may risk losing.
b. Run e.g. Crystal Diskinfo (free) set to alert you to disk degradation using SMART parameters vs thresholds.
Early warning system.