New Apple pen gen 2, will not connect or charge.

Since your iPad Pro 11” (2nd gen) does indeed support Apple Pencil 2, the issue is almost always related to either software corruption or a problem with the magnetic charging/pairing area. Updating to the latest iPadOS was the right first step, but sometimes the update itself introduces a hiccup in Bluetooth services or drivers.

Here’s what I recommend trying step by step:

1. Forget the Pencil completely: Go into Settings > Bluetooth, find the Apple Pencil, and “Forget This Device.” Then restart your iPad.
2. Wipe the flat side of the Pencil and the iPad’s charging edge with a lint-free cloth slightly dampened with water (oil or dust can prevent charging).
3. Snap the Pencil onto the iPad and wait. If you see “Connected” but no charging indicator, leave it on for 5–10 minutes just in case it’s a very low battery.
4. Go to Settings > General > Transfer or Reset iPad > Reset > Reset Network Settings. This clears out stubborn Bluetooth issues.
5. If a friend or store can let you test, this can quickly confirm whether the Pencil or the iPad’s charging strip is at fault.

If none of that helps, it’s worth booking a quick Apple Store or authorized service visit. Sometimes the magnetic charging coil inside the iPad can fail, and unfortunately, that requires professional repair.

Your description indicates that the Pencil has successfully paired with your iPad while docked with the iPad's magnetic charging dock

Be aware that if your Pencil has been set-aside for an extended period, unused and uncharged, the Pencil battery may be irretrievably damaged through deep discharge. In common with all Li-ion batteries, they must always have some level of charge.

The tiny internal Li-ion battery is susceptible to permanent/irreversible damage through being left discharged for long periods. Even some “new” pencils can exhibit signs of failure out-of-the-box, especially if they are “old stock”. 

It is essential that if you have an Apple Pencil that you charge it regularly - whether used or not - so as to protect the battery from deep-discharge. Do not allow a pencil to remain in low-charge state for any period of time - as the internal battery will fail, rendering the Pencil useless. Setting aside an unused Pencil, for extended periods, is a recipe for premature death of the Pencil battery.

If the Pencil Battery has failed, the only remedy is to replace the Pencil. If the battery has failed and your pencil is within its one-year warranty, you should look to having it replaced by your retailer or at an Apple Store. If purchased directly from Apple, in most countries/regions you can unconditionally return the Pencil for exchange or refund.

Gentle warming of the Pencil (such as placing on a hot water radiator), prior to attempting charging of the Pencil, can sometimes resurrect a dead Pencil battery.