What are your reasonable options for backing up a 16TB NAS in 2021?

External Hard Drive?

Pros:

• Interface Portability. You do not need any new software or hardware.
• Ability to reuse older hardware: Assuming you have a used drive large enough to hold all your backups.

Cons:

• Interface instability: USB3 drives especially are bad at this. The adapters are usually not designed to handle the multiple hours of uptime necessary to complete backing up multiple terabytes of data.
• Transfer speeds: Most USB3 drives are not designed for performance. Even custom enclosures with reasonable drives in them usually struggle to keep a sustained write speed of 100MB/s.

Tape?

Pros:

• Very reliable: Most tapes will probably outlast the drives that created them.

Cons:

• Expensive: LTO-4 drives are several grand apiece, including used models. LTO-5 or LTO-6 is even more expensive, and LTO-5 or LTO-6 will be needed for most users with a NAS.