With the default config require("headlines").setup() and everything (nvim, nvim-treesitter, markdown parser, markdown_inline parser, ..) up-to-date, I get the following behaviors from markdown.

block quote + list

code

* list item
  > quote line 1
  > quote line 2. The bar is misplaced and ">" is not hidden.

Result

code block + list

code

* item 1
  ```
  code block
  ```
* this item's bullet is hidden

Result