HTML tables not correctly included in embed HTML from a embed qmd

Bug description

This is related to #7210 and I've tested it on Quarto version 1.5.22 and 1.4.358. The captions now work for outputting knitr::kable tables but not with other table types (gt)

Steps to reproduce

1. in the terminal i made a new project, quarto create project manuscript
2. here's the index.qmd

---
title: "Test of embedding tables"
format:
  html:
    toc: true
---

Hello world

```{r}
#| label: tbl-one
#| tbl-cap: This is normal gt table

gt::gt(head(mtcars))

```

embed with gt

{{< embed notebooks/table.qmd#tbl-two >}}

embed with kable

{{< embed notebooks/table.qmd#tbl-three >}}

3. here's the notebook i want to embed in this path notebooks/table.qmd

---
title: "Notebook"
---

```{r}
#| label: tbl-two

gt::gt(head(mtcars))
```

```{r}
#| label: tbl-three

knitr::kable(head(mtcars))
```

here's the result

Expected behavior

The gt table should render in the document. In total I should have two gt tables and one kable

Actual behavior

The gt table from the child document notebook/table.qmd does not render while the kable table does. Only the tbl-cap renders

Your environment

• IDE: Rstudio, Windows 11

$version
[1] ‘2023.12.1.402’

$long_version
[1] "2023.12.1+402"

$release_name
[1] "Ocean Storm"

Quarto check output

$ quarto render
[1/2] notebooks\table.qmd
[2/2] index.qmd

Creating MECA Bundle
  2 article files
  22 source files
  2 notebooks
  2 other files

Output created: _manuscript\index.html


FAA3303@DOHLTTUM2107608 MINGW64 ~/Projects/personal-repos/test
$ quarto check
Quarto 1.5.22
[>] Checking versions of quarto binary dependencies...
      Pandoc version 3.1.11: OK
      Dart Sass version 1.69.5: OK
      Deno version 1.37.2: OK
[>] Checking versions of quarto dependencies......OK
[>] Checking Quarto installation......OK
      Version: 1.5.22
      Path: C:\Program Files\Quarto\bin
      CodePage: 1252

[>] Checking tools....................OK
      TinyTeX: v2024.02
      Chromium: (not installed)

[>] Checking LaTeX....................OK
      Using: TinyTex
      Path: C:\Users\FAA3303\AppData\Roaming\TinyTeX\bin\windows\
      Version: 2023

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

[>] Checking Python 3 installation....OK
      Version: 3.10.13 (Conda)
      Path: C:/Users/FAA3303/AppData/Local/miniforge3/python.exe
      Jupyter: (None)

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

[>] Checking R installation...........OK
      Version: 4.2.2
      Path: C:/PROGRA~1/R/R-42~1.2
      LibPaths:
        - C:/Program Files/R/R-4.2.2/library
      knitr: 1.45
      rmarkdown: 2.10

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