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I love the "south at the top" variants! :D
Numerous equal-area projections already exist. It's unclear what makes this one better.
I have always found it a bizarre idea that we allegedly judge a country's importance by it's size on a Mercator projection map. Does anyone really think Greenland is the most important place in the world? Europe is tiny, yet the kind of people to complain about it will also complain about the outsized importance of it. Africa, which is apparently a victim of such projectionism, is also placed in the middle because of where the arbitrary Greenwich meridian goes.
Doesn't bringing up the topic of different projections still act as a good reminder that maps of spherical planets will always have one issue or another?

Graphical representations of things have an impact on preception and then by proxy on thinking. Maintaining aome degree of general awareness of these impacts leads to better thinking that is more reflective of the ground truth.

Some would call that "woke" with bad intentions, but hey, they got an agenda and that agaenda doesn't care about facts.

The name of the island I live on (Amami) is misspelled. That does not give me a great deal of confidence about the rest of the map.
Small quibble: the Isle of Man, Guernsey and Jersey all have "(UK)" appended. They are not actually part of the UK, but British Crown dependencies. Possible confusion (as with most things British and overseas).
The choices of cities, towns, and lakes to display in New Zealand is rather strange. The biggest lakes in the South Island are missing, and Napier, Rotorua, and Nelson are shown while some bigger places aren't.

Is it similar for other countries?

It's not the size of the landmass that counts, anyway. It's how you use it.
If you want kids to understand what the world looks like, put a physical globe in every elementary classroom. This will give them a starting point from which to understand how different flat projections work.
While we’re discussing map projections - Tupaia’s map of the south seas deserves mention as a reminder that every map has a baked in set of assumptions and use cases: https://knowablemagazine.org/content/article/society/2021/re...

(For further exploration of the ideals of maps, James C Scott’s Seeing Like a State is excellent treatise for pulling the boundaries of the question back.)

I see the page about "Data Sources", but would be interested in more info about how it was made. Do people use "auto-layout" algorithms for placement of labels? Or maybe it is just started with something basic and have to do lots of refinements by-hand?
"Gulf of Mexico" is correctly labeled!