My iPhone 7 battery continues to drain very quickly, but if I shut it down and repower up, it comes back to the original charge. However, it then drains quickly again.

Have you checked the battery health? Chances are that this battery may be near the end of its useful life and needs to be replaced.

Ref:

• iPhone Battery and Performance - Apple Support
• About recalibration of battery health reporting in iOS 14.5 - Apple Support

Is this battery the original that came with this iPhone or is it a replacement? For the latter, did Apple or you/third-party replace it?