Does an Apple Watch series 9 with cellular have its own phone number?

Unless you set up the Apple Watch for a family member, your iPhone has to have a carrier plan that supports the Apple Watch:

Set up Apple Watch for a family member - Apple Support

Apple Watch - Carriers - Apple

If you are going to have to pay for an Apple Watch plan, why not just get a supported iPhone carrier plan and pay the extra $10 per month to include the Apple Watch?

Apple Watch Family Plan

Set up Apple Watch for a family member - Apple Support

Set up a family member’s Apple Watch - Apple Support

Some limitations: Cannot receive SMS/MMS messages, as that depends on a fully paired iPhone. Messaging is pretty much limited to Apple's Messages, unless the messaging service provides an Apple Watch app. Alarms, alerts, notifications on the iPhone are not sent to the Apple Watch. Apple Pay via a credit card is not available. Also not available: Medications, respiratory rate, irregular heart rhythm notifications, ECG, AFib History, Cycle Tracking, Sleep, Wrist Temperature, Blood Oxygen, Walking Steadiness, Audiobooks, Camera Remote, News, Shortcuts, and the double tap gesture.