Do I need an active subscription for those free 2 months of GamePass?

If "The Neighbourhood" is a online multiplayer mode, you need to have an active Gamepass Core or Gamepass Ultimate subscription to play online. It does not matter where you bought the game from, all paid games on Xbox require a Gamepass subscription to play online. Free to play games do not require a subscription to play online.

PUBG and the Elder Scrolls Onlime is available to download for free with an active subscription of Gamepass.

You will also need an active Gold subscription to be able to play them as they are both online games.

None of these suggestions solve the problem.

The account has never had a GamePass for PC subscription.

The account is part of a family group because it is a child account.

We are trying to use the GamePass for PC offer that is on the top banner of the Xbox app on my child's PC. We click the link, enter our billing information and get the error message: "You don't have permission to do this. An adult in your family needs to turn on recurring billing for you." We follow the instructions to "turn on recurring billing" but those instructions require an active subscription. The subscription can't be activated without recurring billing. Recurring billing requires an active subscription. It is a endless loop of frustration.

If activating a free trial of GamePass for PC is not an option on a child account, please stop advertising for it on child accounts. Or fix the bug in the system that created this loop so that you can give the next generation of GamePass subscribers a sneak peek at this platform.

All games on gamepass are free as long as you have an active subscription

Additional info:

I also cannot launch Sea of Thieves. It tells me that I need to "renew gold" which is absolutely preposterous, considering 1) I own the game, and 2) I have an active subscription to GamePass Ultimate, and 3) to my knowledge "gold" does not exist anymore.

Gold does still exist. It's required to play online on any paid game, but it is no longer needed for free-to-play games. However, you are correct that if you still gave an active Ultimate subscription, you do still have Gold.