Can’t connect Apple Pencil (1st gen) to iPad (A16) using adapter

No, the two Pencil adapters (and corresponding connecting cables) are functionally not equivalent - and can not be used in the manner that you appear to be attempting. Sorry, but you can't use the "shorter" Lightning/Lightning Adapter to connect your iPad A16 with the first generation Apple Pencil.

The iPad User Guide clearly describes how to pair/charge the first generation Apple Pencil with an iPad A16:

Pair and charge Apple Pencil (1st generation) with iPad - Apple Support

As illustrated, you must use the longer Lightning/USB-C Adapter with a USB-C/USB-C cable to pair and charge the Pencil with the iPad A16.

See:

Pair Apple Pencil with your iPad - Apple Support

There are two different (and easily confused) versions of Apple Pencil charging Adapter.

New first generation Pencils now ship with this special adapter in the box along with the Pencil. However, some older stock purchased from retailers may lack the USB-C to Lightning adapter - and may instead have an older Lightning to Lightning Adapter.

For owners of older first generation Pencils, or for “old stock” new Pencils, the new special adapter can be purchased directly from Apple as an accessory.

https://store.apple.com/xc/product/MQLU3ZM/A

You're very welcome.

You're not the first - and are unlikely to be the last - to question the viability of the combination that you have tried.

USB-C and Lightning are electrically and technically completely different connection interfaces. Not every combination of Adapters and cables will work; simply finding a combination of cables and adapters that physically connect does not guarantee that the devices that either end can successfully communicate.