Noto Color Emoji font characters don't display as expected

[decision-making-mike]

What I did

1. I downloaded the NotoColorEmoji-Regular.ttf file from https://fonts.google.com/noto/specimen/Noto+Color+Emoji
2. I put it in the ~/.local/share/fonts directory.

Behavior

1. In the Wikipedia article on the Symbols and Pictographs Extended-A Unicode block, in Google Chrome, possibly all the emojis that are there display as expected.
2. Unexpectedly, when I print all the characters from that block in MATE Terminal, I don't see any emojis whatsoever. It looks like that:
   
3. Here is the script I used to generate those results (in Bash):

   for x in {7..9} {A..F}
   do
       for y in {0..9} {A..F}
       do
           printf " | U+1FA${x}${y}: \U1FA${x}${y} "
   
           if [[ "$y" == 3 ]] || [[ "$y" == 7 ]] || [[ "$y" == B ]]
           then echo
           fi
       done
   
       echo
   done

4. Just to make it clear, I know that Chrome and MATE Terminal use the font file by the fact that when I rename it, some emojis don't display anymore, and some display as "boxes" with Unicode code points within (what's the name of this character?).

Questions

1. Most importantly, why don't the emojis display as expected (or not at all, it's hard to judge for me what better describes this behavior)?
2. How can I make them display as expected?

Environment

1. When I do

   mate-terminal --version

   I get

   MATE Terminal 1.28.1
   

2. GNOME Fonts tells me the font file holds version 2.051 of the font.
3. https://github.com/googlefonts/noto-emoji/releases tells me this font version supports version 17.0 of Unicode.
4. chrome://settings/help tells me I use version 142.0.7444.162 of Google Chrome.

---

PS. Just to note, this issue is a follow-up to my question on StackExchange: https://unix.stackexchange.com/questions/801315/why-doesnt-mate-terminal-display-the-heart-hands-emoji-u1faf6