Algebraicity of critical values of adjoint $L$-functions for ${\rm GSp}_4$

We prove an algebraicity result for certain critical value of adjoint $L$-functions for ${\rm GSp}_4$ over a totally real number field in terms of the Petersson norm of normalized generic cuspidal newforms on ${\rm GSp}_4$. This is a generalization of our previous result arXiv:1902.06429.