If you didn't back it up you are probably out of luck. Unless you can find a local repair shop that is willing to jury rig temporary power to it long enough to transfer. Good luck.
You can't pull data off a dead phone, even if you pull the storage out and connect it to a reader you will find the information is encrypted and of no use. This is all done for security, it wouldn't be safe to have personal data on a phone otherwise.
Welcome to Android Central! Just to be sure -- you've gone to contacts.google.com on your computer browser and checked if your contacts synced there? This is why I always recommend to save your contacts to your Google account (which syncs automatically), rather than the local Phone account (which doesn't sync anywhere). You might also want to check your Samsung account, in case the contacts were synced there.
Similarly, go to your Google Photos in your computer browser and see if your photos may have synced there.
If you can't or won't use the cloud to sync your important data on a regular basis, then it's up to you to make sure that data is backed up somewhere else on a regular basis. Phones can fail (or otherwise have bad stuff happen to them), so if you only keep your important data on your phone without any backup, that's asking for trouble.