That is a very specific usage: ‘The Government’ as a proposer of law, Parliament as approvers. Outside of a PPE course it isn’t how the term is used and I think you know this.

In day to day use the government (small g) can be talked about as comprising anyone involved in governance, from the PM down to local councillors, depending on context

Calling people out on this based on a technicality is like correcting people when they say ‘speed’ instead of ‘velocity’, and it’s super irrelevant in a thread about MPs acting in a political capacity

You seem to be confused. The phrase ‘government official’ refers to anyone acting on behalf of the government, including backbenchers. This could even include unelected aides, spokespeople or some civil servants.

You’re thinking of the cabinet. You do not have to be in the cabinet to be a ‘government official’.

As a fellow brit, these Americans correcting you are right.

Yup

https://en.m.wikipedia.org/wiki/Make_Everything_Great_Again