{bslib} output not rendered properly in html documents

[JosiahParry]

Bug description

When including bslib components they are not always rended appropriately. For example navsets lose a fair amount of their styling.

Quarto Output:

bslib output from inline in the notebook or console

Related: #6081

Steps to reproduce

---
title: "Untitled"
format:
  html:
    theme: cosmo
---


```{r}
library(bslib)
plot_tab <- navset_card_tab(
  title = "Plots",
  nav_panel(
    "Panel 1",
    card_body("Here is some body")
  ),
  nav_panel(
    "Panel 2",
    card_body("Here is some body")
  )
)

plot_tab
```

Expected behavior

I expect the styling from bslib to persist in the rendering of the quarto document. I would understand if the bootstrap theme from the quarto doc is used instead of one specified in the bslib code itself. However, it would be nice if the same styling can be used from the bslib code.

Actual behavior

Quarto Output:

Your environment

R version 4.3.0 (2023-04-21)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS 14.0

Quarto check output

Quarto 1.4.489
[✓] Checking versions of quarto binary dependencies...
Pandoc version 3.1.8: OK
Dart Sass version 1.55.0: OK
Deno version 1.33.4: OK
[✓] Checking versions of quarto dependencies......OK
[✓] Checking Quarto installation......OK
Version: 1.4.489
Path: /Applications/quarto/bin

[✓] Checking tools....................OK
TinyTeX: (external install)
Chromium: (not installed)

[✓] Checking LaTeX....................OK
Using: TinyTex
Path: /Users/josiahparry/Library/TinyTeX/bin/universal-darwin
Version: 2022

[✓] Checking basic markdown render....OK

[✓] Checking Python 3 installation....OK
Version: 3.8.12 (Conda)
Path: /Users/josiahparry/Library/r-miniconda-arm64/envs/geo/bin/python
Jupyter: (None)

  Jupyter is not available in this Python installation.
  Install with conda install jupyter

[✓] Checking R installation...........OK
Version: 4.3.0
Path: /Library/Frameworks/R.framework/Resources
LibPaths:
- /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/library
knitr: 1.42
rmarkdown: 2.21

[✓] Checking Knitr engine render......OK

[dragonstyle]

Thanks for reporting this issue! In the case of navset, this is tracked here:

#7657

I'm going to close this in favor of that issue, which is connected to an upstream bslib issue. If you have other non-navset examples, please feel free to open additional issues!