I managed to get the paring and list working by hacking the file /recalbox/scripts/moonlight/Moonlight.sh

# cp /recalbox/scripts/moonlight/Moonlight.sh /tmp/
# diff -Nru /recalbox/scripts/moonlight/Moonlight.sh /tmp/Moonlight.sh
--- /recalbox/scripts/moonlight/Moonlight.sh    2024-03-28 23:44:14.000000000 +0100
+++ /tmp/Moonlight.sh   2024-05-19 15:19:16.836516762 +0200
@@ -1,10 +1,12 @@
 #!/bin/bash
 SCRIPT=`realpath $0`
-SCRIPTPATH=`dirname $SCRIPT`
+SCRIPTPATH=/recalbox/scripts/moonlight
 source "${SCRIPTPATH}/moonlight.inc.sh"
 source "${SCRIPTPATH}/generic.inc.sh"
 #source ./moonlight.inc.sh
 #source ./generic.inc.sh
+echo '{ "device": "/dev/dri/card1" }' > /tmp/eglfs.json
+export QT_QPA_EGLFS_KMS_CONFIG=/tmp/eglfs.json

 mlGameList=$moonlightConf/gamelist.txt
 mlRomDir=/recalbox/share/roms/moonlight

Info from https://forums.raspberrypi.com/viewtopic.php?t=361454

# /tmp/Moonlight.sh find
Listing available GFE servers :
GFE Host pct(192.168.99.50)  running GFE 3.23.0.74
You can now run the following commands:
  /tmp/Moonlight.sh pair pct
  /tmp/Moonlight.sh init pct

but later we get the same problem:

from the log /recalbox/share/system/logs/frontend.log

[2024/05/19 15:11:54.424] (INFO ) : [Run] Configgen Output:
Running command: XDG_DATA_DIRS=/recalbox/share/system/configs SHELL=/bin/sh RUNLEVEL=S MESA_LOADER_DRIVER_OVERRIDE=vc4 PWD=/ _=/usr/bin/python SDL_VIDEO_GL_DRIVER=/usr/lib/libGLESv2.so HOME=/recalbox/share/system LANG=de_DE.UTF-8 SDL_NOMOUSE=1 TERM=linux label=RECALBOX SDL_VIDEO_EGL_DRIVER=/usr/lib/libEGL.so INIT_VERSION=sysvinit- SHLVL=3 CONSOLE=/dev/console PATH=/sbin:/usr/sbin:/bin:/usr/bin PREVLEVEL=N /usr/bin/moonlight stream 192.168.99.50 Desktop
Process exitcode: -6
00:00:00 - Qt Info: Unable to detect Wayland or X11, so EGLFS will be used by default. Set QT_QPA_PLATFORM to override this.
00:00:00 - Qt Info: Setting display mode by default. Set QT_QPA_EGLFS_ALWAYS_SET_MODE=0 to override this.
00:00:00 - Qt Critical: drmModeGetResources failed (Operation not supported)
00:00:00 - SDL Info (0): Compiled with SDL 2.26.5
00:00:00 - SDL Info (0): Running with SDL 2.26.5
00:00:00 - Qt Info: Successfully loaded translation for  "de_DE"
00:00:00 - Qt Fatal: Cannot create window: no screens available

I think I know why we get the error...

When I manually execute the command, I get:

# moonlight --pin 3343 pair 192.168.99.50
00:00:00 - Qt Info: Unable to detect Wayland or X11, so EGLFS will be used by default. Set QT_QPA_PLATFORM to override this.
00:00:00 - Qt Info: Setting display mode by default. Set QT_QPA_EGLFS_ALWAYS_SET_MODE=0 to override this.
00:00:00 - Qt Critical: drmModeGetResources failed (Operation not supported)
00:00:00 - SDL Info (0): Compiled with SDL 2.26.5
00:00:00 - SDL Info (0): Running with SDL 2.26.5
00:00:00 - Qt Info: No translation available for  "C"
00:00:00 - Qt Fatal: Cannot create window: no screens available
Aborted

@Training-Day

today I also downloaded a fresh copy of recalbox 9.2-experimental for rpi5 and also wanted to connect it to my working moonlight.

I also get the same error:

# /recalbox/scripts/moonlight/Moonlight.sh find
Listing available GFE servers :
GFE Host pct(192.168.99.50)  running GFE 3.23.0.74
You can now run the following commands:
  /recalbox/scripts/moonlight/Moonlight.sh pair pct
  /recalbox/scripts/moonlight/Moonlight.sh init pct
# /recalbox/scripts/moonlight/Moonlight.sh pair pct
Hostname mode
pct(192.168.99.50) /recalbox/share/system/configs/moonlight/moonlight-pct.conf | /recalbox/share/system/configs/moonlight/keydir-pct
When PIN is asked on your PC, enter the number ----> 3343 <----
/recalbox/scripts/moonlight/Moonlight.sh: line 35:  4840 Aborted                 moonlight --pin "$pin" pair "$mlIp" > /dev/null 2>&1
ERROR mlPair() : could not pair. Exiting ...

I had no way to input the PIN on the sunshine webpage - moonlight on the recalbox shell immediately returns the error.