bslib::bs_themer() is not compatible with inner fixedPage

I upgraded to the latest version of bslib and can confirm that the problem persists.

Describe the problem

Using bslib::bs_themer() fails when the UI uses fixedPage() in its code.

Here is a minimal reproducible example:

ui <- fluidPage(
    title = "Test",
    theme = bslib::bs_theme(),
    fixedPage("test")
)

server <- function(input, output) {
    bslib::bs_themer()
}

shinyApp(ui, server)

And the error message:

Listening on http://127.0.0.1:5053
Browsing http://127.0.0.1:5053
Warning: Error in : `bslib::bs_themer()` requires `shiny::bootstrapLib()` to be present in the app's UI. Consider providing `bslib::bs_theme()` to the theme argument of the relevant page layout function (or, more generally, adding `bootstrapLib(bs_theme())` to the UI.
  42: stop
  41: bslib::bs_themer [/tmp/RtmpQ1Pvgh/R.INSTALL26981d69cd6522/bslib/R/bs-theme-preview.R#363]
  40: server [#2]
   3: runApp [/tmp/RtmpVRGFGf/R.INSTALL271ae265d30250/shiny/R/runapp.R#388]
   2: print.shiny.appobj [/tmp/RtmpVRGFGf/R.INSTALL271ae265d30250/shiny/R/shinyapp.R#565]
   1: <Anonymous>
Error : `bslib::bs_themer()` requires `shiny::bootstrapLib()` to be present in the app's UI. Consider providing `bslib::bs_theme()` to the theme argument of the relevant page layout function (or, more generally, adding `bootstrapLib(bs_theme())` to the UI.

The issue can be fixed by using bslib::page_fixed() instead of fixedPage(). However:

• The error message is misleading
• bslib appears compatible with using bslib::page_fixed() or fixedPage() interchangeably with no impact, so finding out the root of the issue is challenging

Some more tests/infos:

• The bug appears with shiny::fixedPage() or shiny::fluidPage(). And can be fixed using bslib::page_fixed() or bslib::page_fluid().
• The bug appears only when fixedPage() is used internally. As you can see in my example, I'm using a fluidPage in my initial call, and this one does not create the bug. It is only when used inside this function.
• Using a fixedPage() inside a fluidPage() is relatively standard, typically to create a full-width header at the top of the page, and then a fixed-width container with the content of the page. Despite the misleading function naming, they don't create a page but a container, and we can have containers inside containers.

Session Info

> sessionInfo()
R version 4.3.3 (2024-02-29)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Debian GNU/Linux 12 (bookworm)
Matrix products: default

BLAS/LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.21.so;  LAPACK version 3.11.0
locale:

[1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C               LC_TIME=fr_FR.UTF-8

[4] LC_COLLATE=en_US.UTF-8     LC_MONETARY=fr_FR.UTF-8    LC_MESSAGES=en_US.UTF-8

[7] LC_PAPER=fr_FR.UTF-8       LC_NAME=C                  LC_ADDRESS=C

[10] LC_TELEPHONE=C             LC_MEASUREMENT=fr_FR.UTF-8 LC_IDENTIFICATION=C
time zone: Europe/Paris

tzcode source: system (glibc)
attached base packages:

[1] stats     graphics  grDevices datasets  utils     methods   base
other attached packages:

[1] shiny_1.8.1.1
loaded via a namespace (and not attached):

[1] crayon_1.5.2      vctrs_0.6.5       cli_3.6.2         rlang_1.1.3       renv_1.0.5

[6] promises_1.3.0    jsonlite_1.8.8    xtable_1.8-4      glue_1.7.0        htmltools_0.5.8.1

[11] httpuv_1.6.15     sass_0.4.9        fansi_1.0.6       jquerylib_0.1.4   tibble_3.2.1

[16] fastmap_1.1.1     yaml_2.3.8        lifecycle_1.0.4   memoise_2.0.1     compiler_4.3.3

[21] fs_1.6.3          pkgconfig_2.0.3   Rcpp_1.0.12       later_1.3.2       digest_0.6.35

[26] R6_2.5.1          utf8_1.2.4        pillar_1.9.0      magrittr_2.0.3    bslib_0.8.0.9000

[31] tools_4.3.3       mime_0.12         cachem_1.0.8

Start in R/bs-theme-preview.R around the bs_themer() check shown in the error trace, and compare how nested shiny::fixedPage() and bslib::page_fixed() contribute UI dependencies. Reproduce the minimal app, then add or update a regression test showing that bs_themer() works with an inner fixedPage() and reports the correct result.