MRP vignette / case study: questions concerning interaction between "male" and "age"

In the MRP vignette / case study, the model is formulated as follows:

cat_pref ~ factor(male) + factor(male) * factor(age) + 
    (1 | state) + (1 | age) + (1 | eth) + (1 | income)

My first question is if this shouldn't be

cat_pref ~ factor(male) + factor(male) : factor(age) + 
    (1 | state) + (1 | age) + (1 | eth) + (1 | income)

since factor(male) * factor(age) is equal to factor(male) + factor(age) + factor(male) : factor(age) and thus adds non-varying main effects for the age groups (which already have varying intercepts).

My second question is if it wouldn't be better (in terms of consistency) to use the following model:

cat_pref ~ factor(male) + 
    (1 | state) + (1 + factor(male) | age) + (1 | eth) + (1 | income)

i.e. to use varying slopes for male. Or was there a reason for having varying intercepts for age, but non-varying male:age interactions?

Start with vignettes/mrp.Rmd and compare the two model formulations described in the issue. Resolve the statistical rationale for the age effects and male-by-age interaction, then update the vignette and its explanation so the chosen specification is clear and internally consistent.