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The maximum color quantization you can do on this image without huge information errors is something like:

• 1x yellow-brown for stars / streamers / shorts / socks
• 1x brown for tree base (though it might be better to remove the base to save a color)
• 1x red for baubles / hat / sweater / shoes
• 1x green for tree
• 1x blue for hair (potentially you could merge the tree color if you want to really push it)
• 1x skin tone for skin
• 1x pink for mouth
• 1x black for lines
• 1x light yellow for background

Which is 9 total colors. This would also require living with aliased text ( c r u n c h y ), since it would be data-expensive to add extra shades of gray. At that point you're no longer making a low-quality copy of the original - you'd basically be making a pixel art version of it since you can't afford any colors for anti-aliasing and gradients.

Here's an example PNG with 9 unique colors and some pretty simple patterns without huge information density: https://files.catbox.moe/bj0acl.png

Even that's 1,847 bytes! (i.e., basically 2KB)

Edit: I made a big (in hindsight, obvious) mistake by forgetting I can literally just change the bit depth of the image when saving, so the example I've provided is actually very inefficient by comparison. Valmond has set me straight.