By a process of trial, error, and trawling through the Quarto documentation, I use the following at the top of my Quarto documents:
---
title: "This is the title"
description: This is the description
author: "A Person, B Another, C Someone"
date: '`r format(Sys.Date(), "%B %d, %Y")`'
date-format: "D MMMM YYYY"
bibliography: bibliography.bib
I had not used the !expr version in the YAML header, so it might work in some other way. TAML syntax is quite picky...
!expr is something valid with R yaml package when YAML is parsed with R. This syntax is working in R Markdown YAML header because rmarkdown is just R. But in Quarto it will work only for R document with YAML code chunk configuration (Quarto – Using R)
Inside YAML header of Qmd document, Quarto offers some keywords / alias and config to do the same, like date: today you found. Everything is here: Quarto – Quarto Dates and Date Formatting
If you mean like `r variable` syntax from knitr, you can do that in Qmd document using R too. There is no such inline syntax for Python as of now.
Quarto has also a mechanism for variables defined in YAML file - see Quarto – Variables