Oh wow. That really sucks. I wonder if you put a door stopper or something like that under the door, it would prevent someone from opening it from the outside. I'm sure there's some kind of product out there for situations where a renter isn't allowed to drill holes for a new lock or something like that.
Edit: I did find this item on Amazon. https://www.amazon.com/dp/B008YGQSOO?th=1
I agree with the idea of a travel lock, but that looks a bit flimsy. This guy demos a strap for the deadbolt and door handle that probably would work better.
I always use this for travel: https://www.amazon.com/gp/product/B008YGQSOO/
You could probably get away with malicious compliance using that.
Also I highly highly suggest getting door security hinge pins and installing on your door. It is extremely easy to install. It isn’t illegal, and vastly increases the security of your doors: https://www.amazon.com/Door-Hinge-Security-Screws-3-Pack/dp/B01DG0TZ1A/
what is the actual hardware on your door like? If you have a deadbolt that you want to keep latched or a handle rather than a knob, get a "Super Grip Lock deadbolt strap" so you're protected from under/over door attacks. If you're not allowed to change the locking mechanism but you don't think the landlord would notice something minor, take out the screws in your strikeplates and replace them with the longest screw you can find/fit. If the door fitment is crap or you have hinges installed wrong, put jamb pins in. Most important is to make sure your windows don't have anything appealing visible from the outdoors, so just stay organized and vigilant. Also, depending on how "shoestring" you're really talking, a cheap camera like maybe a WYZE or a trail-cam can be had for ~50-100 with an SD card.
If you have a weapon keep it on you/get a kitchen knife. Search your house thoroughly...check all cabinets, closets, crawl spaces. If you still don't feel comfortable after that call the non emergency number for your local police and ask them to do a walk through because of a suspected break in. There is a cool tool that you can get for the door if it has a dead bolt...I've actually been looking at getting one myself. (I'll Post the link when I get to a computer). Otherwise there are a ton of other safety brackets and such to better secure the door and make sure this doesn't happen again.
This thing! ://www.amazon.com/Super-Grip-Lock-by-EasyComforts/dp/B008YGQSOO