For a generalised linear model, the deviance is defined as $$D(\boldsymbol{Y} | \hat{\boldsymbol{\mu}}) = 2 \phi \sum_{i=1}^n \{\ell(y_i|y_i) - \ell(y_i|\hat{\mu}_i)\} = \sum_{i=1}^n d_i.$$ Here $\ell$ is the log-likehood, $d_i$ is the contribution of the $i$-th observation to the deviance, $n$ is the number of data points, $\hat{\mu}_i$ are the fitted values and $y_i$ are the observed values. The deviance residual is defined to be $$e_i^d = \text{sgn}(y_i - \hat{\mu}_i)\sqrt{d_i}.$$
Some sources claim the deviance residual to be normally distributed. See for example Agresti's Categorical Data Analysis (Section 6.2.1), Dunn and Smyth's Generalized Linear Models With Examples in R (Section 8.3.3) and this paper (Introduction). However, this SE post mentions that deviance residuals are not necessarily normally distributed.
I am quite confused about this. The argument for the normality is that the deviance is asymptotically chi-squared distributed, and so the signed square root of individual contributions must be normal. That sounds reasonable but it is at odds with (for example) the SE post.
Could someone please shed light on this? Can we take the deviance residuals to be normally distributed? If not, how do we interpret the normal QQ plot produced by R when looking at the diagnostic figures for a GLM (i.e. from plot(glm))? Thank you!