If you insist on 'secure' firmware, you're fighting uphill and probably going to be disappointed with the ecosystem out there. Tunnel back to your home network to access cams if that worries you.
I recommend either Ubiquiti or Reolink cameras, both are power-over-Ethernet. Both offer an app that allows connecting back to your equipment. UI will require their Protect software running on one of their local platforms in your house with storage on 1 or more disk drives, while Reolink offers direct storage on microSD on the camera itself, capped at 256GB.
Unfortunately my house is not wired for Ethernet and it's a rental so I can't install it. Wireless is a must and security is obviously important for wireless. But I think you are correct that I will be disappointed by what's out there.
Unfortunate. Reolink even has wireless cameras, but they will require a DC input, so you'd need an outdoor electrical outlet if you can't drill any holes and sneak either a power or UTP Ethernet cable.
Given the strict physical requirements, you might be looking at battery-backed wireless cameras of the type often found on Amazon, but afaik they will never offer the local storage or control you want.
I will say that surprising things can be accomplished with small drilled holes and a fishtape. Your risk tolerance and how nice the rental are obviously very important factors.
I used a Reolink Argus with a battery and Wi-Fi connection. The one I used is probably EOL now, but a quick look at the site shows even solar chargeable options. So, it is possible.
I've got a Reolink Argus 2E which look like it's been replaced by the 3E, but it works great without any wired connection to the house. I've got it solar powered and strapped to a tree, unprotected by the elements. 2 years and still working.
I recommend either Ubiquiti or Reolink cameras, both are power-over-Ethernet. Both offer an app that allows connecting back to your equipment. UI will require their Protect software running on one of their local platforms in your house with storage on 1 or more disk drives, while Reolink offers direct storage on microSD on the camera itself, capped at 256GB.