new watch but what does the recharge plug into?

You can use any USB-C port on a personal computer.

You can use the USB-C charger from a recent Macbook Pro, iPhone, or iPad.

If you have an older Apple Watch, you can use the charging puck and power brick.

You can purchase any manufacture's USB-C charger from any retailer, such as Best Buy, Staples, Amazon, etc....   A 20watt or higher charger will enable Apple Watch Series 7 Fast Charging.  But any size USB-C charger will do.

You can get a USB-C to USB-A adapter and use any USB-A port or charger (this will not enable Series 7 fast charging as the USB-A standards are limited on how much power they can provide).

You should not have buy anything if you have had ANY previous iPhone, 3rd Party or Apple chargers at all that used to work with previous Apple purchases.

If you go to Apple Store and pose this question to the official Apple Site clicking on charger and cable accessories you will see 4 compatible chargers. 1 is the ginormous 22w USB C wall charger plus 3 other USB A wall chargers. All of which you probably have.

I have owned three iPads and three iPhones. The charger cord that I have for my new Apple Watch SE doesn’t fit into any of the adapters. So, am I being told that I have to spend more money for an adapter for $300 watch?