rsync with X11-Forwarding does not set DISPLAY?

Some context:

• I have some services running on my Debian server, and from time to time I want to make a backup of the relevant data
• I have a backup directory on the server, which I update manually by stopping the services, copying the data into that directory (using rsync -Payz --delete --recursive, which preserves metadata and avoids unnecessary copies), then relaunching the services
• I want to have a copy of the backup directory on my laptop, and keep it updated
• To that end, I want to run something like rsync -Payz --delete --recursive user@server:backup .
• The main difficulty here is that many of the files have root as an owner and rsync isn't allowed to move them without sudo (the services run in containers, and those permissions make sense at the container level, but at the host level the system considers the host's root is the owner)
• To create the sever backup I can simply call sudo rsync, but for the copy on my laptop I have to tell rsync to run sudo rsync on the server and forward the password request to the client, which brings us to the current issue

What I've done:

I've followed the advice from this post, so the full command I'm running is

rsync -Payz --delete --recursive -e "ssh -X" --rsync-path="sudo -A rsync" user@server:backup .

• --rsync-path="sudo rsync" is used to run rsync with sudo rights on the remote

• --rsync-path="sudo -A rsync" is used so that sudo relies on ssh-askpass to get the password

• -e "ssh -X" enables X11-Forwarding so that ssh-askpass can ask me to type the password on my laptop

The issue

• This used to on my old laptop (a MacBook), but doesn't on my new one (running a Manjaro distribution). Given that the linked post's comments say it's working on Ubuntu, I'm assuming I need to change something in my configuration, or maybe I'm missing a dependency or something, but I have no idea what or why
• The error I get is the following:

Error: Can't open display: 
sudo: no password was provided
sudo: a password is required
rsync: connection unexpectedly closed (0 bytes received so far) [Receiver]
rsync error: error in rsync protocol data stream (code 12) at io.c(231) [Receiver=3.2.7]

• When I run the command with -e "ssh -Xv", the following lines appear that seem to be the issue

debug1: X11 forwarding requested but DISPLAY not set
debug1: Sending command: sudo -A rsync --server --sender -logDtprze.iLsfxCIvu . backup
Error: Can't open display: 
sudo: no password was provided
sudo: a password is required
debug1: client_input_channel_req: channel 0 rtype exit-status reply 0
debug1: client_input_channel_req: channel 0 rtype eow@openssh.com reply 0
debug1: channel 0: free: client-session, nchannels 1
rsync: connection unexpectedly closed (0 bytes received so far) [Receiver]
Transferred: sent 2176, received 2464 bytes, in 0.2 seconds
Bytes per second: sent 9432.6, received 10681.1
rsync error: error in rsync protocol data stream (code 12) at io.c(231) [Receiver=3.2.7]

so apparently when rsync runs ssh -X here, the DISPLAY variable is left unset

• If I run ssh -X 'echo $DISPLAY however, it does displays localhost:10.0, and running ssh -X user@server 'sudo ls' does ask me the password as expected (through a window titled "OpenSSH Authentification Passhrase Request")
• I believe that means that the problem is in the interaction between ssh -X and rsync, not the X11-Forwarding itself, but I don't get what I'm doing wrong

I can only suggest you trace the environment being passed through rsync as follows. Add option -n to do no transfers, and use some /tmp/dummy file. Prefix the command with strace using option -v to see the environment during execve() calls, -f to follow children, and -o log to output to some log file.
For example,

DISPLAY=:0 strace -vf -o /tmp/log rsync -n -Payz  --delete --recursive \
 -e 'ssh -X' --rsync-path='sudo -A rsync' user@server:/tmp/dummy /tmp/dummy

Looking through the log file you should see something like

5261  execve("/usr/bin/ssh", ["ssh", "-X", "-l", "user", "server", 
 "sudo -A rsync", "--server", "--sender", "-nlogDtprze.iLsfxC", ".",
 "/tmp/dummy"], ["DISPLAY=:0", "SHELL=/usr/bin/bash", ...] <unfinished ...>

(one long line).
Beware, you may need to ignore many execve's of ssh that are
attempted and fail as each directory in the current PATH is tried.
In this example output, 5261 is the process id.

The execve() system call of /usr/bin/ssh shows
the arguments to ssh in the first array [...],
and the environment passed to the command in the second array [..."DISPLAY=:0"...].
Ensure "DISPLAY=:0" is in this second array.

If it isn't, then look earlier in the file for the first execve() of rsync to see
if DISPLAY is in the env there. You should find something like:

5624  execve("/usr/bin/rsync", ["rsync", "-n", "-Payz", "--delete",
 "--recursive", "-e", "ssh -X", "--rsync-path=sudo -A rsync", 
 "user@server:/tmp/dummy", "/tmp/dummy"], [...,"DISPLAY=:0",...]) = 0

You can add a second -f to strace to get separate log files, one for
each process, rather than all intermixed.

If it is in the first execve("/usr/bin/rsync", and not in the later
execve("/usr/bin/ssh", that would indeed suggest that rsync has
deliberately removed it from the environment. Perhaps this is some sort of
new security feature?

To work round it, create your own shell script "ssh" in your PATH that
simply does

#!/usr/bin/bash
export DISPLAY=:0; exec /usr/bin/ssh "$@"