Any hint to actually do the most important big tasks, during the deep work session, instead of smaller, also necessary but less critical tasks?

Don’t distract yourself, in doing so you’ll loss motivation and become bored.
Stay focused by ignoring distractions, stay foucus and stop when you need to

Be clear on what the priority is. And just start. (I wouldn’t say I’m at expert at this). Sometimes any progress is good progress, other times you need to just start the big thing! I find starting the big thing with something less intimidating like brainstorming or making an outline, etc, helps it be less daunting and then you have a starting place to build from.