Does my Galaxy s7 need a battery replacement?

Hello, I’m new to the hobby of electronic repairing and this is my first project. I have a Samsung Galaxy s7 with a severely cracked touchscreen, cracked back glass, and a booting issue. I’m not yet confident in diagnosing it as of needing a replacement battery, so I would highly appreciate other opinions. I will be writing the device’s malfunctions and my attempts so far to solve them below:

• Once the phone has fully charged, it is initially operational while plugged in to the charger.
• After it has been unplugged and used for a bit, it has powered off. An attempt to power it back on (while plugged back into the charger) has entered it into boot loop.
• I’ve pressed the volume up key, power button, and home button simultaneously as to enter recovery mode. Instead, it has entered a different sort of loop, going between “recovery booting..” in small blue font at the top, to an installing updates screen, to a sad android man saying “no command”, and repeat.
• Eventually, after about a minute in this loop, it finally enters Android Recovery. I’ve wiped the cache partition and rebooted the phone without a hard reset.
• Currently, it continues going through the original boot loop.

* Also, I need to mention that through the short time I have been testing the phone, the battery percentage will plummet from a full charge at a rapid pace. This is what has led me to believe it is in need of a battery replacement. However, I am unsure of if a new battery will solve all of these tricky booting issues, or if there is something in trouble with the motherboard or other hardware. Any advice or help would be greatly appreciated.