How can I minimize the carbon emissions of my software applications?

Biggest wins are often achieved by starting from the demand side and try to figure out how to reduce demand. Think about the what jobs your software applications do. Are there other lower-carbon ways to do those jobs?

Simple non software example: I want to reduce carbon emissions of my dining. Current habit is to dine out at restaurant with friends 50% of time, cook at home 50% of time. Dining does multiple jobs: providing basic nutrition, letting me catch up with friends over shared activity. Dining at restaurant is more energy & carbon intensive than dining at home. Job of catching up with friends can be done by lower carbon activity such as getting a coffee. New routine could be dine out at restaurant 10% of time, cook at home 90% of time. New non-dining habit of coffee to do job of catching up with friends.

Very different result compared to thinking about "how do i minimise the carbon emissions of the restaurant i dine at"

I think there's a bigger opportunity to minimize emissions by working on digestion and flatulence.

First, start with correct data on how much emissions they are currently responsible for. Then, see if your efforts will be useful. Aka due diligence

Not exactly, like this, but somewhat like this:

https://xkcd.com/1205/