Strategies to avoid burn out due to systemic lack of time
I find myself on the brink of burnout. What are effective strategies to avoid burnout and optimize time management in academia, having as a premise that it is literally impossible to wholly fulfill all of one's commitments?



Find a therapist. Really. There is no shame in getting help when dealing with a difficult life situation. This won't reduce your workload, but a therapist should be able to give you custom tips for better managing it.
Learn to say no. Fundamentally, if your workload has been ever increasing, this is a good sign that you are bad at saying "no" to tasks. This is an extremely important skill to learn, and a therapist may be able to help you learn it if you can't do it on your own.
Start delegating. In addition to saying "no" to tasks, start delegating (parts of) the tasks that you still agree to carry out. Remember how you as a PhD student sometimes needed to help the senior people in your team with organisational varia, reviews, literature searches, etc.? You are now one of those senior people. Don't be shy to ask the students you help supervise to lend a hand with your tasks.
Accept that sometimes there is too little time to get everything done (or: accept that sometimes some things can't be done well in the time that is available). Many of us have this little perfectionist in us that requires us to (a) come through on everything we promised at some point, and (b) do everything in the best possible quality. In real life, there is usually just enough time to do some things well, and the rest either not at all or in mediocre quality. This is not your fault, and it is best to accept that sometimes you will give a presentation that's not very well prepared, or be unable to submit to this workshop even though you promised the chair a month ago.
Be aware of your priorities. Relatedly, be aware of what you personally really value and want to do right. For me, being badly prepared for teaching is a no-no. For you, it may be skipping a major paper or grant deadline. Note that I specifically said your priorities, not necessarily the priorities of your postdoc advisor or students. While in an ideal world you want to take their preferences and needs into account as well, if push comes to shove you can't consistently ignore your own priorities over the needs of others. Four years into your postdoc you should easily be senior and independent enough that you can push back if your mentor wants to force her/his own agenda onto you (if this is not the case, I suggest getting the heck out of there).