between two worlds

Hello sniktajoy, it is the Non-British citizen who applies, though of course the British spouse has to help, to furnish documents, etc etc. The British spouse is the applicant's "sponsor."

The whole application is made by the non-UK applicant, it is he or she who is the "I" of the application. And a US spouse has to be in the US when s/he does it.
It sounds from Megan's story as if she, like me, was in America with her husband and they did the whole process together, which is the easiest way.

The govt websites are confusing because they talk about the foreign spouse seeking settlement as going to join the UK one…but often the UK one is not yet back in the UK and will only return to reside there at the same time as the foreign spouse enters. (Because they are married and living together abroad, of course!)
This is normal and it is fine from the government's point of view. I wish they would make it clearer in the guidance!

Megan in her brilliant summary of their process says "applied for the settlement visa for my husband" --maybe because she did most of the work in finding forms etc?! Or she means "we applied." But strictly speaking it was her US husband who applied.

As I said above, it is the non-UK/non-EU spouse who applies.
The British spouse is the sponsor and the applicant must explain their relationship etc in the application.