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I don't understand what that Wikipedia entry is supposed to describe. Are those proposed, or already predicted composite atoms, or have they been already found?
The article only mentions Muonium in passing -- I guess it's only somewhat exotic? -- but I can assure you that it's very real. Chemically it acts as a light isotope of hydrogen, and the interaction of the (anti)muon spin makes it useful for probing reactions in otherwise problematic environments -- for example, supercritical water, where the pressure chamber needed for hundreds of atmospheres of pressure gets in the way of most sensors.
I legitimately thought this was going to be an "exotic skin" for the atom text editor.
The header of the wikipedia article mentions that because the resulting particles are usually unstable, the exotic atoms typically have short lifetimes.

If someone has the time to point to the research, the article would be massively improved by mentioning the typical lifetimes of each of the listed exotic atoms.

A "short lifetime" could be nanoseconds or could be years when you compare it to the traditional lifetime of the non-exotic version of the atom and knowing what is typical for each exotic atom would be good information to have at a glance.

The half-life of approximately 15 minutes for free neutrons is considered long. It's actually the longest for any sub-atomic particle if I recall correctly.
I think protons would like to have a word with you.
Proton decay has never been observed, afaik.

Edit: that's still the case. Since protons can not decay in the standard model, actually observing it would be huge.

The half-life of those exotic atoms are almost the same as the particles themselves, if not the exact same, so about 2.2us for the muonic atom.