When it comes to increasing fitness for everyday tasks, the first things that come to mind are usually classical endurance activities, like low intensity steady state (LISS) cardio or sometimes even high intensity training (HIIT). A dreaded proposition for any lifter that is looking to improve fitness for every day tasks.
Luckily, the answer could be nearer to the truth. While there are certainly benefits to cardiovascular training (such as not dying), for every day tasks the benefits of cardio quickly taper out, because, surprise surprise, most of the tasks we face are not low intensity steady state. Even the stereotypical "getting winded from walking up stairs" will not be improved much by typical endurance training, as even if you run up tens of flights, you are done after at most a few minutes and for only a handful of flights of stairs, the whole activity doesn't take more than a few seconds.
Most things just have this sporadic nature. You need quite some force for a short period and then there is usually some leisurely pace in between. Usually it is not even maximal force, unless of course, you are very weak. So it's also not high intensity. It's just medium output for a short period of time with some rest in between.
Consequently, one of the very best ways to improve work capacity and fitness for everyday life, are sets with moderate weight for a couple of reps in a compound exercise with pretty short timed rests. The rest periods should be around the 1 minute mark and I feel that much shorter than 45 seconds reduces the weight to a point were it stops being appropriate and much longer than 90 seconds usually reduces the benefits for work capacity.
A very systematic and prefabricated way to do this is the inverted Juggernaut method. But you can also just do squats for 5 reps at 70% with 1 minute rest until the last set is pretty heavy. Depending on your paradigm, you can just do this as back-off, e.g. when training with RTS style prescriptions, x5@8 and then 10% load drop with 60s rest periods. The exact protocol does not really matter, as long as the weight is appreciable, the rest period around the 1 minute mark and the reps somewhere between three and eight reps.
This makes a good training session. And even one such session a week can carry you a long way through phases with other emphasizes, so just because your periodization laid out twelve weeks of hypertrophy and strength, you can still be fit at the end of it.
If you have a nice separate timer, this is a good way to just get in the flow of doing an exercise and you might even end up with a nice pump. You probably won't have much time to check for technique in between sets. Also note that the exercise should be big. Bench and push press is fine, but I already feel like that this timed effort doesn't do much for me with pressing. And as much as I love my kettlebell, they are not the tool for this job. These are already more refined tools for more athletic endeavours.