This would be my advice, first slow down a smidge. There is a lot going on here so there is no particular order to my advice.
First, start working from home, don't ask just do. Inform your line manager that one morning a week you will work from home. Then build to more. Don't put in a request just do it. If the business is over working you without asking you just WFH.
Only 20% of your work is recognised by the business it's a variant of Pareto's law, so bear that in mind.
13 people to manage, well that means you can delegate 1/13th of your work to each of them. This is a time to be tough with yourself, don't hold on to it delegate it.
The people management stuff 1-2-1s can be as short as you ok?, do you need any support? And these are my concerns! Try to reduce it to minutes. Also does it need to be at the frequency HR likes to think it should be.
Document reading, delegate it to your team and tell then "Do I need to make a decision" that can be done under the guise of professional development.
Send people off to meetings on your behalf.
If your overburdened and under staffed something will give, make sure it's not you.
Look at your own workload and say, do I need to do this?
Start reading Forbes. Inc, and hbr for tips and tricks to life hack your actual work load.
Also manage up, identify the key people you have to satisfy, not the needy demanding ones, but the ones who are decision makers.
Learn to keep a journal of times
7:40 left home
8:10 read doc X
8:45 @ desk
9:05 had coffee caught up with Bhavna
9:15 reviewed emails
9:17 answered slack
10:00 team meeting
...
It doesn't have to be exact and you don't have to do it there and then but at the end of the week review it and start to see the patterns of time eating.
Put off needy people till the last minute and make sure when you do interact with them 10 mins later youve got a meeting to get to.
Start to build slack into your workload, you do this with a combination of delegation and task analysis.
Take up some stress management and self care exercises, take a 5 mins break ever hour, floor walk, and casually chat with people. Every couple of hours walk out the building and around it. Get fresh air and sunlight.. if someone can't wait 10 mins for you to decompress and are snarky, then it's more about them than you.
Learn to push back, sorry my team is to busy right now come back to me in x. Add wiggle room to schedules and deadlines.
Compartmentalise, when at home only think about work for 45mins after 8pm and use that time to plan your immediate needs. Do not catastrophise. That's for your bosses to do and only react if it is business threatening
Build in zero thought time at home and at work. After looking at your actual daily work from the note book I suggested above. Identify times in the day when you can switch off and I mean really switch off, no personal stuff or social media. Clear down your mental desk.
Overall, you need to look out for yourself, no one else will as they have many issues too which they are keeping to themselves. Building in self care and flexibility into you work life balance is critical to keeping it balanced.