do you have applecare one yet?

Apple introduces AppleCare One, streamlining coverage into a single plan - Apple

Add AppleCare coverage to your Apple device - Apple Support

The time limits to purchase this plan has expired for me, so I'm considering the purchase of a new watch just to be able to get this new plan and getting my iPad and iPhone covered under it, along with the new watch.

That is correct: When you purchase a new product from Apple, you can start an AppleCare One plan.

My iPhone is under 2 years old, and my iPad is under one year old so theoretically I should be eligible, right?

Yes, if they are in good condition. They want to avoid claims for existing conditions. With AppleCare One, customers can add products they already own that are up to four years old¹ if they are in good condition³.

1. Devices must be less than four years old, and headphones must be less than one year old. Only devices in the customer’s Apple Account can be covered under AppleCare One.

3. To verify “good condition,” products may be required to undergo a diagnostic check using a customer’s iPhone or iPad, or at an Apple Store, prior to being added to the plan.