Linux

PPAs are flawed and limited to the Debian/Ubuntu ecosystem. They're a security issue as you really need to trust to the person or group who has set up the PPA (yet many people just added PPAs for all sorts of random software based on a Google search). They need to be maintained which is variable depending on the size of the project and for developers they're only a route to support part of the entire Linux ecosystem. They can also conflict with the main system provided packages and repost which can break entire systems or break upgrades (happened to me on Mint, and I needed to do a complete system reinstall to remove legacy package conflicts).

They've fallen out of fashion and rightly so.

There are other ways to get software to users. Arch has its AUR which is basically a huge open repo. OpenSuSE has its OBS which is also a huge open repo. These are also not without their risks as it's hard to curate everything on such an expansive repo. However others can take over packages if the original developer stops updating them, and you can see how the package was built rathe than just download binaries which allays some security concerns. They are also centralised and integrated into the system, while PPAs are a bit of a free for all.

Flatpaks are a popular alternative now - essentially you download and run software which runs in a sandbox with its own dependencies. Flatpaks share their sandboxed dependencies but it does lead to some bloat as you'll have system level libraries and separate Flatpak versions of the same libraries both installed and running at the same time. However it does mean software can be run on different systems without breaking the whole system if library dependencies don't match. There are issues around signing though - flathub allows anyone to maintain software rather than insisting on the original devs doing so. That allows software to be in a Flatpak that might otherwise not happen but adds a potential security risk of bad actors packaging software or not keeping up to date. They do now have a verified tick in Flathub to show if a Flatpak is official.

Snap is the Canonical alternative to Flatpak - it's controversial as it's proprietary and arguably more cumbersome. The backend is closed source and in canonical control. Snaps are also different and for more than just desktop apps and can be used to in servers and other software stacks, while Flatpak is focused only on desktop apps. Canonical arr also forcing Ubuntu users to use it - for example Firefox only comes in a snap on Ubuntu now. It has similar fundamental issues around bloat. It has mostly the same benefits and issues as Flatpak, although Flatpaks are faster to startup.

Appimage are another alternative way to distribute software - they are basically an all-in-one image. You are essentially "mounting" the image and running the software inside. It includes all the libraries etc within the image and uses those instead of the local libraries. It does and can use local libraries too; the idea is to include specific libraries that are unlikely to be on most target systems. So again it has a bloat associated with it, and also security risks if the Appimage is running insecure older libraries. Appimage can be in a sandbox but doesn't have to be, unlike Flatpak where sandboxing is mandatory - which is a security concern. Also Appimages are standalone and need to be manually updated individually while Flatpaks and Snaps are usually kept up to date via an update system.

I used to use PPAs when I was still using Ubuntu and Mint. Now I personally use Flatpak, and rarely Appimages, and occasionally apps from the OBS as I'm on OpenSuSE Tumbleweed. I don't bother with snaps at all - that's not to say they don't have value but it's not for me.

Edit: in terms of permissions, with Flatpak you can install Flatseal and manage software's permissions and access per app. You can give software access to more locations including system level folders should you need to or all devices etc for example. I assume you can do the same with snap but I don't know how.

Also you can of course build software form source so it runs natively , if you can't find it in a repo. I've done that a few times - can be fiddly but can also be easy.