To cut to the chase, Flatpak is nice to have, but isn't a complete replacement, and the other suggested "replacement", Pacstall, targets Ubuntu instead of base Debian. If you want more detail, read the spoiler:
spoiler
I use EndeavourOS as my daily driver, so I'm used to the sheer convenience of the AUR. However, I'm not a fan of how that convenience is tied to a continually-changing rolling release distro. This becomes especially apparent whenever a major KDE update comes out, or the Arch Linux people decide to make yet another big change.
Debian is the other main distro I use. I mostly install it on systems I don't intend to use often, but recently I started dual-booting it on my main desktop. I like how slowly things change in the Debian world, and if it were easier to run uncommon software on it, I'd probably use it more.
I know Debian can use Flatpak, and while it is nice to have, it's not a complete replacement for the AUR. The other "replacement" MPR/Makedeb's developer suggested is Pacstall, but that's for Ubuntu and not base Debian. If Ubuntu were the same distro it were back when 20.04 came out, I wouldn't be opposed to using it, but Ubuntu's gone to shit since then.
EDIT: Inb4 Distrobox too.
EDIT2: The reason I want an AUR equivalent is convenience. Yes, I commit the cardinal sin of using an AUR helper when I use EndeavourOS. I like being able to install things and have them integrate into my normal system package management without having to manually set up scripts.
One reason I use Debian is that the repo is so large most things are there. If they are not or what is there is too old I use primarily flatpak and appimage.
Curious what you do not like about Ubuntu? I admit I am not crazy about it these days but one reason we uٌse it for some systems is the supported software. We are at 24.04 and only uprgade every 4 years but it seems to work fine.
Ubuntu started locking certain security updates behind Ubuntu One a few years ago. They also won't stop pushing Snap over native packages.
Yes I hate the snap for everything stuff.
Regarding security updates, are the missing ones critical? I have been ignoring ubuntu one.
They added an option for enterprise to extend security patches support for unsupported old distros, and then gave it free to users too behind a pro account. But you don't need it unless you're on a very old version of ubuntu.
I guess other thing Ubuntu One provides is kernal hot patching which I do not care about.
I think Debian has a similar option though provided by a third party.
I'm not sure tbh, but the idea of locking any security updates behind One irritates me.
My reason for hating Ubuntu is snaps