How can I transfer data from my watch to my new phone if I don’t have my old phone?

Don’t you have an iCloud or iTunes backup of that old iPhone? Your iCloud or iTunes backups from an iPhone include backups of all the Apple Watch data for the watch used with that iPhone.

Because without a backup you’re simply not going to be able to recover that data. Without a backup or the device to make one, the data is lost to you.

Back up your Apple Watch - Apple Support

Click this link and then the embedded link If you don't have your old phone --> How to pair your Apple Watch with a new iPhone - Apple Support

My 8 year old phone battery is completely dead. It will not recharge only a slice of a red charging bar. I plug it in and it won't recharge the battery. So I'm just going to buy the new SE to replace my old SE original. How do I get the info from my old phone to new one if I can't charge it?

If you have been backing up your phone, you can restore from the backup or at least most recent backup. If you haven't backed up your phone and it is dead, you won't be able to restore from the backup, if there isn't one.

Anything you synced with iCloud, such as Photos, text messages, etc., will come over to the new phone assuming you had those services turned on previously. You can restore all your apps as long as you use the same Apple ID on the new phone as you did on the old phone.