Script to send a Control Shift Tab key press combination to the foreground app, if this is Chromium it will switch tabs.
NOTE: It may be necessary to send an Alt Tab key press to bring the desired app or app window to foreground.
Create a script:
sudo vi /opt/scripts/chromium-switch-tab.sh
#!/bin/bash
export DISPLAY=:0.0
export XAUTHORITY=/home/pi/.Xauthority
/usr/bin/xdotool key Ctrl+Shift+Tab
Update the permissions
sudo chown pi.pi /opt/scripts/chromium-switch-tab.sh
sudo chmod u+x /opt/scripts/chromium-switch-tab.sh
sudo chmod +x /opt/scripts/chromium-switch-tab.sh
Test:
/opt/scripts/chromium-switch-tab.sh