You plan sounds interesting but that is not how Apple Watch works. However, at a practical level you can still achieve the same result. Considering only the cellular version of Apple Watch, explanation below.
Provided your network has setup the account correctly the eSIM in a cellular Apple Watch always mirrors the phone number of the paired iPhone. The watch will actually be configured with its own eSIM and phone number but this is only used internally by the cellular network for call routing and administration. By cellular smoke and mirrors calls to your iPhone will also be pushed to your Apple Watch, and calls made from your watch will appear to come from your iPhone's number. This is always true, 24/7 365 days a year regardless where your iPhone is, and regardless whether the iPhone is switched on or not.
This means your cellular Apple Watch will behave rather like a traditional "extension phone". If you are carrying the phone you can use either the watch or the phone to make calls. If you are away from the phone just use the watch, there is no need for a different number.