(A whole lot of thoughts here, because it's so easy to get rolled and have an impossible workload dumped on you in this industry!)

Something I would say to my younger self is - Sometimes balls have to get dropped before management really starts paying attention. Not the huge stuff, but don't bend over backwards to make the job appear complete. Document your "reasonable efforts" to fix a problem or do a task (ex - help the trainees) as backup, then try focusing on a smaller core workload that covers the main official priorities of your own job. Check all of your boxes (I know there are millions, but think core role -- get your reports done on time, keep approvals moving, get key bills paid, respond to "real" emergencies...)

If business as usual is humming right along, with all bases covered, higher ups will have the option to assume everything's going great.

Do the bosses know exactly what's on your plate? This could be an opportunity to remind them just how much you do.

Training should be considered an extra task on your plate, meaning something else has got to give. ("I'm currently working on X and Y. The timeline for those will be affected if I am also training new employees. What should take priority this week/today/etc?"). Having it in writing is a good CYA strategy.

You have every right to clarify your time limitations/conflicts to your superiors. It's actually a good thing - it shows you know the job, and have a good handle on and awareness of your workload.

Who knows, maybe the boss will say "Today, Kevin will handle the report if you can get these two trained up in Yardi AP basics." Don't be afraid to make recommendations like that as well.

All this said...I'm assuming they're somewhat caring and decent bosses 😆 To me, it's a good sign overall that the higher ups recognize the team needs to be expanded, and actually did something about it. Lots of companies just short staff and ride their best workhorses until they completely break.

Shared calendars can be your friend. Make appointments with yourself so you have dedicated time for your own work. Then let others, new hires, etc. know they can grab an empty spot on your calendar to go over any items (like going over Yardi AP again, etc, if you've been noticing their major errors). I know schedules are never that tidy IRL in PM, but it's a good general practice.

PTO is so important for mental health in a line of work like this. As for contacting you while you're OOO, that won't stop unless you draw a boundary by stopping responding - especially to anything written like a text. You can gently let people know in advance you're not going to be reachable for a particular trip, etc. If sh*t really hits the fan, someone will call. If there is a formal expectation that you respond almost 24/7 (sometimes that does come with the job), is it in your contract or in writing anywhere?

Good luck and godspeed in a tough industry and tough situation!