You're right with your observations. I read some place that at the end of 2019 there was about 36,000 different Christian groups/denominations around the world. Not all churches teach from God's Word, but make things up as they go along. They sometimes do that to make their church more attractive and to draw new members in from other churches, to get tithing money. When a church and administration fails to teach from God's Word, they sometimes don't have the ability to address some issues, including mental health. God has a special love for persons who struggle with many types of mental and physical problems. We remember Isaiah 41:10 "Don’t be afraid, for I am with you. Don’t be discouraged, for I am your God. I will strengthen you and help you. I will hold you up with my victorious right hand."
If we know a Christian who has a mental illness and is not being comforted by the teachings of their church, we can carefully suggest to them and their family that they might wish to find a church that will help them - in complete harmony with the psychological and medical help that they are already receiving.