Path of the Image in Question is hard coded as 'resource:///org/gnome/shell/theme/process-working.svg' and this is from the .gresource file being used.

This resource file could be different for login screen and desktop session.

Assuming you are using Default Ubuntu 20.04

you need to edit/replace the file process-working.svg from the .gresource file.

for Default Ubuntu 20.04 /usr/share/gnome-shell/theme/Yaru/gnome-shell-theme.gresource file is the one to edit.

I have gone through this process and replaced process-working.svg file with some .svg's and fell in a login loop.

the default process-working.svg file is like this.

and its properties are like this.

There seems to be a trick with svg images, Its a single svg image with different spinners. So I googled and got some 512 x 32 pixels with similar gnome-shell theme and could successfully change the spinner.

Getting/Creating the SVG is going to take much time.. So I used vanilla gnome's spinner and default Yaru's

Yaru's

Vanilla GNOME's

Edit:

have edited the original process-working.svg file with inkspace like this for testing purpose keeping the original size 512 x 32 px with svg format and tested it.

For Automation Purpose, the below script can be used.

Requirements

1. First keep your preferred .svg file (512px X 32px) process-working.svg in /tmp directory.


2. install the package libglib2.0-dev with below command

sudo apt install libglib2.0-dev

then save the below script in a plain text file as pwsvg.sh (process-working.svg)

#!/bin/bash



source="/usr/share/gnome-shell/theme/Yaru/gnome-shell-theme.gresource"

backup=$source.BAK



pkg=$(dpkg -l | grep libglib2.0-dev >/dev/null && echo "yes" || echo "no")

if [ "$pkg" == "no" ]

then

echo "

-------------------------------------------------------------------------------------------------------------------------------------

Sorry, the package 'libglib2.0-dev' is not installed. Install the package 'sudo apt install libglib2.0-dev' and then run this Script.

For now, Exiting...

-------------------------------------------------------------------------------------------------------------------------------------"

exit 1

fi



cd /tmp



if ! [ -f "process-working.svg" ]

then

echo "-----your preferred .svg file 'process-working.svg' not found in /tmp folder. put the process-working.svg file in /tmp directory first.-----"

exit

fi



if [ "$UID" != "0" ]

then

echo "This Script must be run with sudo"

exit 1

fi



# take backup of original resource file

if ! [ -f $backup ]

then

cp $source $backup;

fi



for a in $(gresource list $backup); do

    b="${a/#/org/gnome/shell/}"

    mkdir -p $(dirname $b)

    gresource extract $backup $a > $b

done



mv -f process-working.svg ./theme/



FILES=$(find "theme" -type f -printf "%P

" | xargs -i echo "    <file>{}</file>")



cat <<EOF >"theme/gnome-shell-theme.gresource.xml"

<?xml version="1.0" encoding="UTF-8"?>

<gresources>

  <gresource prefix="/org/gnome/shell/theme">

$FILES

  </gresource>

</gresources>

EOF



cd theme

glib-compile-resources gnome-shell-theme.gresource.xml

mv -f gnome-shell-theme.gresource $source

echo " Reboot to see the changes "

run the command sudo bash pwsvg.sh and reboot.

in case anything wrong, from any tty
replace the edited gresource file with the backup one which is /usr/share/gnome-shell/theme/Yaru/gnome-shell-theme.gresource.BAK

sudo mv /usr/share/gnome-shell/theme/Yaru/gnome-shell-theme.gresource.BAK /usr/share/gnome-shell/theme/Yaru/gnome-shell-theme.gresource

Tested in Ubuntu 20.04.2