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I'm wondering if leaving this feature enabled drains the laptop battery while it's turned off. I've searched online already but haven't found a conclusive answer.

Fast Startup = NO

https://www.howtogeek.com/243901/the-pros-and-cons-of-windows-10s-fast-startup-mode/

Fast Startup combines elements of a cold shutdown and the hibernate feature. When you shut down your computer with Fast Startup enabled, Windows closes all applications and logs off all users, just as in a normal cold shutdown. At this point, Windows is in a state very similar to when it’s freshly booted up: No users have logged in and started programs, but the Windows kernel is loaded and the system session is running. Windows then alerts device drivers that support it to prepare for hibernation, saves the current system state to the hibernation file and turns off the computer.

Hiberate = NO

Hibernation is kind of a mix between a traditional shut down and sleep mode primarily designed for laptops. When you tell your PC to hibernate, it saves the current state of your PC—open programs and documents to your hard disk and then turns off your PC. Then when it’s time to start it up again all your previous work is ready and waiting for you. Unlike sleep mode, it doesn’t use any power, but it does take longer to start up again.

Sleep mode = YES

in sleep mode, all the above mentioned data is kept in RAM, which is volatile meaning the RAM must be kept powered to retain the data. But sleep mode uses far less power to maintain inactive data in RAM with the operating system doing nothing as opposed to a running system.

No, it doesn't.

Fast Startup works similarly to hibernation therefore all devices are effectively shut down.

With Fast Startup, Windows closes all applications and logs off all users,
alerts device drivers that support it to prepare for hibernation,
saves the current system state to the hibernation file,
and truly turns off totally the computer.

The battery is no longer used during the time that the computer is turned off,
although it should be noted that every battery loses some of its charge over time,
although slowly.
On another note, if Wake-on-LAN
is enabled, then some small amount of power is used for maintaining the
network adapter in a semi-sleep state.

When you start the computer again, Windows does not have to reload the kernel,
drivers, and system state individually. Instead, it just refreshes your RAM with
the loaded image from the hibernation file and delivers you to the login screen.
At this point, Windows is in a state very similar to when it’s freshly booted up.

The conclusion is that Fast Startup does not add to the power drain in any way
more than cold shutdown.

I have has fast start running on two laptops and a desktop here for 4 years. As noted above, there is no power drain because of fast start up when powered off. I can remove the laptop battery when powered off.