If you are using the Distribution package to generate your image, you can ask Yocto to take other recipes to install. This is the case for the Virtual Keyboard.
For example, in a local.conf, you can have this:
IMAGE_INSTALL_append = " \
qtcharts \
qtsvg \
qtvirtualkeyboard \
qtlocation \
qtquickcontrols2 \
qtquickcontrols \
"
Here you can see that for my Qt application, I need to add more Qt libs, and the Virtual Keyboard is included.
2) Did you try to compile the baseline (bitbake st-example-image-qt) without making any change inside?
After that, if it works, we can check what is wrong with your personal project that you try to include inside.
3) As concerns virtual keyboard, this is a library directly developed by Qt, that are integrated by STMicroelectronics. We do not develop this lib and so we do not know which language are exactly usable inside.