@valerijssal - welcome to the forum! Changes to fields are captured in the task’s activity section (down where the comments are, tab over to All Activity). I believe Asana does truncate changes if they’re made in quick succession (e.g., if I change a field value and then go back and change it 5 min later, it will only show the last of those changes).
If you need higher fidelity, you could get this info from the API; probably the easiest way would be to set up webhooks for the tasks of the relevant projects (could be all). That said, you’ll need to do something with that info. I am not sure about whether some of the pre-built Asana tools do this.
There is a feedback request on this topic that you could vote for as a long-term native solution: