From the short description in the advisory, would seem like the attacker can cause the tool to overwrite the file after signature verification.

Of course not, Debian is one of the most robust pieces of software around. They wouldn't do something idiotic like relying on the hash being sent with the payload through the same channel.

I think the idea is that debian distributes the hash themselves through their domain, and mirrors offer the downloads either through http or https. So that you don't need to trust the mirror, you just verify the debian given hash. Only weakness would be a hash collision or a cve like this.

AFAIK this isn't actually true for any distribution. This would break selfhosted mirrors and their clients hosted on airgapped networks, and create a single point of failure for users.

The way packages are validated actually is through the same channel as you download the packages themselves from (IE your mirror), they just are signed with the Debian package signing key(ring), of which only a select few maintainers have authorized private keys for.

This does mean an adversary (whether a MITM if you're using HTTP or malicious operator on the mirror server itself) can technically serve you old versions of an (officially signed) package indefinitely and your package manager would be none the wiser, but otherwise this approach actually works quite well.

The signatures do expire (which is an annoyance when working with snapshot.debian.org).

An attacker might replace a package with a previous one which has a vulnerability. Downgrade attack. Unclear if the apt client will check if version is the expected one after requesting a package.