Well I will try to describe the idea clear:
For comfort I propose to make a table with tasks and their progress in esc menu (I don't know exactly what it is called)
This table can be hidden by pressing the exclamation mark button like button in the main menu
For example:
If you have completed part of a task in past matches, part of the bar will be colored white. If you have full completed the quest in past matches, the color of the bar will be full colored white.
If you have completed part of the task in this match - part of the bar will be colored green. And if you have completed the quest in this match - the bar will be full colored green. The part of the bar that is colored green will not count if you leave the match before you get caught or you finish the game