`as.matrix.projection()` for GAMs: Duplicated linear term

On branch develop (commit 96d8e11d6f0ad0a1f7836c51700cb676b364bee5), this reprex:

options(mc.cores = parallel::detectCores(logical = FALSE))
data("kidiq", package = "rstanarm")
kidiq <- head(kidiq, 45)
fit_gauss <- rstanarm::stan_gamm4(
  kid_score ~ s(mom_iq),
  data = kidiq,
  iter = 500,
  seed = 734572
)

library(projpred)
prj <- project(fit_gauss, solution_terms = c("mom_iq", "s(mom_iq)"),
               ndraws = 25)
colnames(as.matrix(prj))

gives

 [1] "b_Intercept"   "b_mom_iq"      "b_s(mom_iq).1" "b_s(mom_iq).2"
 [5] "b_s(mom_iq).3" "b_s(mom_iq).4" "b_s(mom_iq).5" "b_s(mom_iq).6"
 [9] "b_s(mom_iq).7" "b_s(mom_iq).8" "b_s(mom_iq).9" "sigma"

(so the output matrix includes a linear term for the smoothed predictor) whereas

colnames(as.matrix(fit_gauss))

(correctly) gives

 [1] "(Intercept)"           "s(mom_iq).1"          
 [3] "s(mom_iq).2"           "s(mom_iq).3"          
 [5] "s(mom_iq).4"           "s(mom_iq).5"          
 [7] "s(mom_iq).6"           "s(mom_iq).7"          
 [9] "s(mom_iq).8"           "s(mom_iq).9"          
[11] "sigma"                 "smooth_sd[s(mom_iq)1]"
[13] "smooth_sd[s(mom_iq)2]"

Perhaps the problem is not really with as.matrix.projection(), but rather with project() which would need to project onto the submodel with the smoothed term only (and not an additional linear term), even if solution_terms = c("mom_iq", "s(mom_iq)")?

There's another issue with as.matrix.projection() for GAMs visible here (the smooth_sd parameters) which I'll open a new issue for.

Reproduce the provided GAM example on the stated develop commit, then compare colnames(as.matrix(prj)) with colnames(as.matrix(fit_gauss)). Inspect project() and as.matrix.projection() to determine whether the duplicated linear term comes from projection or matrix conversion. Done means the expected smooth-term-only behavior is established and the returned matrix no longer includes an unintended linear term.