Bluetoothctl is a Linux software part to pair most common bluetooth devices. It should works properly with your controllers too. The first time I tried to pair my Wii U Pro controllers, it gived me a headache. Nothing wanted to work and I had to reproduce different technics to get them paired simultaneously.
I’m not Batocera and/or Linux expert, I will not be able to give you an all-in-one fix. Here is my bluetooth info files content for my 3 controllers :
Device 7C:BB:8A:0A:7B:1D
[General]
Name=Nintendo RVL-CNT-01-UC
Class=0x000508
SupportedTechnologies=BR/EDR;
Trusted=true
Blocked=false
Services=00001124-0000-1000-8000-00805f9b34fb;00001200-0000-1000-8000-00805f9b34fb;
[LinkKey]
Key=5A9DD0FDA89A11B4C0CDF7A01AC8F644
Type=0
PINLength=0
[DeviceID]
Source=2
Vendor=1406
Product=816
Version=1
Device 7C:BB:8A:1D:C9:35
[General]
Name=Nintendo RVL-CNT-01-UC
Class=0x000508
SupportedTechnologies=BR/EDR;
Trusted=true
Blocked=false
Services=00001124-0000-1000-8000-00805f9b34fb;00001200-0000-1000-8000-00805f9b34fb;
[LinkKey]
Key=07DD1A572445892F626E110E4CFEA512
Type=0
PINLength=0
[DeviceID]
Source=2
Vendor=1406
Product=816
Version=1
Device 7C:BB:8A:1F:63:14
[General]
Name=Nintendo RVL-CNT-01-UC
Class=0x000508
SupportedTechnologies=BR/EDR;
Trusted=true
Blocked=false
Services=00001124-0000-1000-8000-00805f9b34fb;00001200-0000-1000-8000-00805f9b34fb;
[LinkKey]
Key=F9112B10247965EFE2D0D748477BB608
Type=0
PINLength=0
[DeviceID]
Source=2
Vendor=1406
Product=816
Version=1
Hope it will help you to compare with your controllers info files and find a clue to solve your issue.