I may be a little dense here but i don't understand "Binding". The issue arises as I had a Mini 3 Pro and a DJI RC controller, then bought a Mavic 3 and found I could use the same controller OK. Could swap between them using Connection Guide (after relevant firmware updates).

For reasons that may seem odd (seeking extra range and brightness), I just bought a DJI RC Pro controller.  It works with the Mavic 3, but I had trouble with the Mini 3 Pro - says device is bound and i could only fly 5 times unless i did something about that.  The on-screen (and most Website ) syntax is odd - talks about binding a device (Drone? Controller?) to an "account.
I had hoped to use the new controller with both drones - but after some test flights I can't use the mini 3 with the new controlloer (RC Pro) any more. Mini 3 Pro does not reliably "Beep" to show going into Pairing mode. Not wanting to mess around trying to find a Web connection while in the bush.  
Questions -
(1) What is actually "bound" to what - (a) A drone to a controller?  (b) A controller to a Drone? (c) Drone to a user account?  (d) Controller to a user account?
(2) Can one Drone be dound to 2 different Controllers? (Yes/No)
(3) Can one controller be bound to 2 different Drones? (Yes/No)

If I decide I have to "Bind" the new Mavic 3 to the new DJI RC Pro controller to get flyaway coverage, how do I do that? Just can't find it.
Thanks for any help.

The drone is bound to the controller so that if it flys away and you get a free replacement no one that find the drone can use it.          You can bind it to one controller at a time,  but you can swap this an unlimited amount of times as long as you have an internet connection.  

Hi there. Thanks for reaching out, and apologies for the inconvenience. Binding the aircraft with the remote controller records the linking relationship between the aircraft and the remote controller. Binding the remote controller you will be using on the aircraft on every flight is necessary. Not binding will result in limited flights and being ineligible to use the Flyaway Coverage replacement.
And here are the answers to your inquiries:
1. The binding required in your case is within the remote controller and the aircraft. You need to bind the remote controller you will be using in a flight to the aircraft (whether the DJI Mavic 3 or the DJI Mini 3 Pro).
2. You can bind/link one drone to multiple remote controllers, but it should be one at a time. Therefore, you must repeat the unbinding process each time you switch controllers.
3. Yes, you can use one remote controller for multiple drones but still needs to be done one at a time.
Please refer to the steps below on how to unbind/bind the remote controller:
1. If you are using the same account for both drones and a prompt appears that you need to bind the remote controller, just select "Change Bound RC." If this does not appear, you need to do it manually.
Note: Ensure you are connected to a network.
2. To manually do the unbinding/binding, go to Profile>Device Management>Value-added service>Unbind RC/Bind New Device.
Unbind the bound remote controller first, then bind the new one you will be using.
We hope this clarifies your concern. Please reach us back should you need further clarification. Thank you, and have a nice day.

DJI Tony Posted at 4-3 23:54
Hi there. Thanks for reaching out, and apologies for the inconvenience. Binding the aircraft with the remote controller records the linking relationship between the aircraft and the remote controller. Binding the remote controller you will be using on the aircraft on every flight is necessary. Not binding will result in limited flights and being ineligible to use the Flyaway Coverage replacement.
And here are the answers to your inquiries:
1. The binding required in your case is within the remote controller and the aircraft. You need to bind the remote controller you will be using in a flight to the aircraft (whether the DJI Mavic 3 or the DJI Mini 3 Pro).

Having to bind and unbind each controller every time you fly is a pain. I wish DJI would fix that.

You can bind two aircraft to one controller like the smartcontroller or pro. but you can't bind one aircraft to two controllers at the same time. You can switch with an internet connection. If you are having problems binding get on chat with DJI and they can walk you through putting two aricraft on your pro.

djiuser_lF8VtFOZvSPw Posted at 11-22 19:48
Having to bind and unbind each controller every time you fly is a pain. I wish DJI would fix that.

Hello, there. We're sorry to hear about the trouble that it may have caused. Rest assured we've taken your feedback for future reference.

I have the original Mavic Mini.  I don't see anywhere on the App where I can bind it or unbind it.  Is the binding something that started with the Mini 2?

fans91eb347c Posted at 1-13 06:51
I have the original Mavic Mini.  I don't see anywhere on the App where I can bind it or unbind it.  Is the binding something that started with the Mini 2?

Hi there. Thank you for reaching out. The DJI Mavic Mini does not support binding/unbinding on the DJI Fly app. This function only supported with the following drones: DJI Mavic 3、DJI Mavic 3 Cine、DJI Mavic 3 Classic、DJI AIR 2S、Mavic Air 2、DJI Mini 2、DJI Mini SE、DJI Avata、DJI Mini 3 Pro、DJI Mini 3、DJI Mini 2 SE、DJI Mini 4 Pro、DJI Air 3. Hope this helps.

I agree. Having to bind unbind use the phone use the controller make sure you have internet connection. It's to much.

This is honestly ridiculous. Please have a better solution.
I use a fpv googles interga and motion 2 with my mini 3 pro. In addition to the DJI RC.
I will be switching remotes mid flight.