This sounds like a hardware issue, it's likely that the shutter wheel is damaged. If you have recently purchased the item, I'd recommend requesting a refund. I would not recommend attempting to repair an issue like this yourself unless you are okay with destroying the camera or really know what you’re doing.
You could try a factory reset the camera software ...
I found similar question was already answered some 7 years ago on this forum
How do I troubleshoot the "Error, press shutter release button again" message on my Nikon?
Maybe it will help.
I am a newbie, don't have any explanations myself.
Panasonic do have an application to help with this if your camera supports WiFi. It's called imageapp and is available for free from Play Store. You can remotely control the camera with this e.g. set shutter speed/exposure/zoom/focus/ISO etc. I've managed remote control from 20 metres. There are no hidden extras that you need to pay for. It works really ...
The self-timer should work. If the camera is still shaking after 2 seconds, even with a big telephoto, you need a stronger tripod. Another choice is to use a separate card as a shutter. Set the camera for a 10 second exposure and hold a piece of cardboard in front of the lens. Trigger the shutter, wait 8 seconds, and take the card away.