Doing bodyweight squats at regular intervals is really good for you. There's been some research into what you should do when you take this recommended 'stand up and move around every 20 minutes you're in your sedentary job' business.
20 (good) bodyweight squats for office workers was found to be the quickest and most efficient way to improve the researchers main KPIs (which I forget).
Basically you can more benefit from doing 20 bodyweight squats that you'd get from going for a 20 minute moderate intensity walk, it takes much less time. More movement in a day overall is better for you.
Training in the gym is training for the gym - you'll get better at what you do in that 15 minutes, but then if you go sit down and work for 10 hours after, it's not helping you much. Having a more active lifestyle with more movement overall throughout your day is better training for your overall life.
15 minutes of weighted exercise is not the kind of way we use our body in our day to day life. We're awake for 16 hours a day where we need to remain upright, which requires stamina. 15 minutes HITT isn't what we need to support our lifestyles. A regular day requires a longer low intensity strength, high stamina, lower intensity.
15 minutes once a day is like doing sprints to train for a marathon - it's a different type of exercise. Marathon runners might add in sprint intervals, but only once they've got their baseline up to the required levels. If you can't run a 5k, then sprint intervals aren't going to get you through 26 miles of steady state running.
You're better off doing your bodyweight squats at lots of regular intervals for functional fitness. Low and slow is a legit entry method into fitness and you're right to start with anything you can stick with. Doing something is always better than doing nothing. It's proved one positive lifestyle change leads to further ones.
Functional fitness will keep you healthy and mobile in later life for longer. Just keep going, you'll know when it gets too easy and you need to add more in. Plus making your 10 minute run part of a 30 minute walk would be better. If you've got it in you, run 2 mins more towards the end of the walk and gradually extend - it'll give you more stamina and one day you'll close the gap.
Not trying to offend or belittle anyone's 15 minute programmes BTW, they absolutely have their place. I've just buggered myself up by having a similar lifestyle and thinking I was doing OK. Recently was read the riot act by an NHS physio explaining all that to me. They even specifically mentioned the 20 squats research and told me to do it.