As an Irish person, in normal speech the word "scheme" has exactly the same shady connotations as it does for Americans. Calling someone a "schemer" is a common insult. I've always assumed the government started using the word in a rare moment of honesty and it stuck.

Or perchance it is the other way around. The word started as official term and over time got shady connotation because can't trust Big Government.

As in "schematic"

In India too, discounts and promotional policies are commonly called 'schemes.' I learned the hard way that in the US, the word has a negative connotation when I asked my rental office about any 'schemes,' they looked at me with total shock.

Similarly, "doubt" has a negative connotation in the US, but I see it often used as a synonym for "question" by Indian speakers of English.

That's hilarious! I hope y'all cleared up the confusion quickly.

Growing up in the UK, we would be sent to a “play scheme” during the school holidays. Weird phrase.

Various variants of english diverted quite a bit since the US became its own country. Like how the US constitution mentions "freedom of speech", which includes many things that aren't just speech as we'd call it, whereas many other countries call the same concept "freedom of expression" because they committed it to writing later.

Another funny difference is the word "corporation" meaning the government in some cases. Like someone living in Belfast could go home from their corporation job to their corporation flat, if they lived in public housing and were employed by Stormont.