Here’s what works for me when I’m not using the RPI headphone jack and no soundcard on my zynthian. Try this: Go back to the webconf and under Hardware select Audio. Then select Hifiberry Dac + Light and check the RBPi Headphones box. Click on Save and then click on REBOOT NOW! Finally click on Reboot.
That indicates the sound subsystem (jack) is not coping and triggering xruns which are failures to process data within assigned time. Each xrun manifests as a click in the audio. Common causes are:
Poor PSU - even though a power supply may be specified with sufficient power delivery it may fail for various reasons including poor quality cable / connector, poor design, etc. This has been the most common cause of this issue even when there is no low power indication.
Use of headphone output - this adds a significant load to the Raspberry Pi and its use is strongly discouraged. It is generally only used for initial testing / assesment before adding a proper soundcard.
Resource hungry engines - some of the sound generators and audio processors in Zynthian are resource hungy and the Raspberry Pi can struggle to run these. Start with something simple like a single Fluidsynth layer with no additional audio or MIDI effects and see if that helps.
Raspberry Pi 3 is underpowered for the current Zynthian. It will struggle with many configurations (see previous point). The RPi4 is substantially more powerful and better suited to Zynthian.
I use a RPi3 for development and suffer frequent xruns. I try to minimise these using all the above points but am yet to get it running smoothly. I can generally get it to run without showing the symbol but there are invariably a few xruns occurring during a session.
best option, especially with the low end pi3, is to use a cheap I2S external DAC like the ones based on pcm5102a (for <5$ on aliexpress or amazon) or for best sound quality (high end pcm5242 chip and a rich connectivity) for a really low price (<30$ in France) https://www.raspberrypi.com/products/iqaudio-dac-pro/
Zynthian supports a bunch of audio devices, look in webconf->hardware->audio. You will for sure find something that fits your needs for a couple of bucks and it will highly improve your musical/sound experience.
USB sound devices works too but they consume more current and are not always Xruns free