What is the assumption for General Linear Regression?

Take Logistic Regression and Beta Regression as an example. Both are using logit(u/1-u) as the transformed response when fitting a linear regression. Logistic has 0-1 as original response, while beta has p which is between (0,1) as original response. As we all know, linear regression requires residual to follow normality, homoscedasticity and No autocorrelation. How about GLM? I know that the original response doesn't have to follow these assumptions, but what about logit(u/1-u)? Does it need to fit the above assumption? Can we simply think transformed_response = X*B as a linear regression with response transformed_response that follow some normal distribution (mean,variance)?