The short answer is that there's no uniform rate- different artists will charge different amounts depending on skill level and perceived value of their work/time.
However I can help shed some light on the different terms being thrown around!
When giving a quote, comic artists typically give a rate by either Page or Panel.
Pages are more geared towards comics that are intended for physical print (i.e. pages in a comic book) and typically contain between 4-8 panels per page.
Some people prefer to give a quote per panel (especially for vertical style comics where pages don't exist), which in case you're not aware, is essentially each picture (speech bubbles exclusive). For example, the episode that you linked had about 67 panels, from a quick count that I did.
If you're specifically looking to make a vertical manhwa style comic, you'll most likely be getting artists giving you per-panel pricing.
So, for an example, say someone said that they would charge $20 per panel for a commission. The cost for the linked episode would then be $20 x 67 = $1,340.