How do I transfer games from old iPad to the new one?

A completely different question...

You don’t transfer Apps between devices. Instead, for compatible Apps that are available within the Apple App Store, you simply download them to the new device. It follows that the new device must be signed-in to the App Store with the same AppleID - as all purchases are tied to the purchasing AppleID.

It might be worth pointing out that Apps are sometimes withdrawn by the respective developer (or sometimes by Apple) from the App Store. Once withdrawn, these Apps cannot be (re)downloaded onto any device.

I hope this is equally helpful.

No - you do not have to pay again. Any Apps purchased against a specific AppleID can be downloaded onto any compatible device that is signed-in to the App Store with that same AppleID.

The only exception to this is some types of in-App purchase... and this may not apply to your Apps.

In-App purchases that unlock additional functionality (for example, an additional purchase to permanently suppresses “advertisements”) are treated just like the App itself; after (re)downloading an App in that such purchase is one-time only; it may be necessary to “restore purchases” to restore the additional functionality upon subsequent App download (see the App for additional details where relevant).

In-App purchases for consumable items (e.g., “coins” in a game) relate to the device where the purchase is made - and are not transferrable or credited to additional devices. You’ll find more details about in-App purchases here:

https://support.apple.com/en-us/HT202023