In general, if you didn’t sync to iCloud and didn’t back up to iCloud and didn’t back up to your computer there is no way to recover the contents of your iPhone.
For all 3, sync options and 2 backup options, they don’t happen until you turn them on.
Contacts normally sync to email addresses, so you can recover them just by logging in to your email account or accounts.
iCloud+ has 2 independent functions. iCloud backups, and iCloud sync. It’s confusing because they both have the same name prefix. But they have no connection with each other. Go to Settings/[your name]/iCloud. You will see a bunch of switches (with iOS 16 or later also tap Show All). When you turn on a switch that data type will sync to iCloud. If you do this on multiple devices that share an Apple ID the selected data will sync to all of those devices.
You can check what was synced by logging in to https://icloud.com.
You can also turn on iCloud Backups. This will back up your phone every night if the phone is plugged in, connected to Wi-Fi and locked.
If this was on, when you reconnect your phone you can restore from an iCloud backup, but you can’t see if you have a backup except by going to iCloud settings on another Apple device, computer or iOS device such as an iPad.
But note that Sync and Backup are independent functions; anything that you sync by the first method will be excluded from the iCloud backups.