I do like the Flathub. I know a lot of Linux purists are against it, but having all these apps in a distro agnostic package is cool.
I'd also recommend flatseal or flatpak-kcm.
That's just because with most distros it's insanely hard to get something you want to use into the distro. It doesn't have to be like that.
Similar (perhaps slightly lower given verification efforts) concerns about integrity/supply chain (who is maintaining this package really? Is it a clean build from the correct source?), but distro independent and often works good enough with some exceptions. Sandboxing is limited but better than nothing.
Once I somewhat understood the process and where everything is on GitHub (fairly transparent with CI stuff) I felt a bit more comfortable with things, but a lot of the store interfaces leave a lot of questions unanswered about the source (location) of the software.
If something is out of date I can usually make a GitHub issue and it'll get sorted soon enough.
Not the worst experience I've had.
The AUR package would still use less disk/network since the flatpak is carrying around effectively its own distro / base image layers. OTOH no sandbox so weigh as you will.
Building a package doesn't imply compilation of the binaries the package is composed from. Packages are meant to provide easier distribution and maintenance.
The distribution aspect of the AUR is useful given the various tooling/helper utilities around it, but I don't see it as more effective than flatpak if you're just using binaries that already exist. While the AUR is a bit more of a direct path, you don't have to worry about system level dependencies changing and breaking the binaries with flatpak (even if that does result in more disk usage as a side-effect).