How do I recover photos and videos from a water-damaged iPhone?

Were you using iCloud Photos on that iPhone?

That's the easiest way to safeguard photos and videos. If you were using it, then you'd be able to see any photos that made it to iCloud by logging into https://www.icloud.com/ – even before you got a replacement phone.

If you were not using it on the phone, it is too late to enable it on that phone now. (It would still be a good idea to use it with any future iPhone that you get.)

If you weren't using iCloud Photos, but you had Settings>Apple ID>iCloud Backup turned on, then you may be able to recover data from the last 30 days or so at iCloud.com. You should look here:

         View and manage iCloud device backups - Apple Support

This requires you to erase everything on your phone and replace it with the backup.

Additionally, you can look here:

         If you're missing photos or videos in the Photos app - Apple Support

There's not much there that hasn't been covered by Zachyy and Servant of Cats

Water damage is irreparable and unfortunately unless those photos were backed up someway, they cannot be retrieved. Nor will Apple service a water damaged iPhone.