You know how made that 2x/3x salary rule?
A jewelry company lol
Engagement rings are the first rung of the scam that is the wedding industrial complex. Don't fall for it.
This. It's a joke and diamonds aren't anywhere near as rare/expensive as they market them to be. Go try and pawn a used wedding ring. You're probably not getting $4K for it.
Find whatever makes you happy and buy that. If it's $200, even better. The wedding industry is a scam. I spent $1700 on my fiancees ring, but only because she absolutely loved it (it was a $5K ring on clearance. I had honestly thought that I wouldn't spend over $1000 on a ring, but she loved this one and she gets daily complements on it, so the $1700 was worth it. If it had cost $400, we wouldn't have cared.)
Also, the whole "wedding rings must be diamonds" was made up by a marketing company. It's not some centuries long tradition. They had a surplus of diamonds and wanted to find a way to get rid of them.