If you count a publisher/vendors latest stable release - then you are correct.
Q: Is there a Manjaro Repository website like the arch one?
A: No, there is not.
Watch the Announcements > Testing Updates thread to get an idea of when the next stable snap occurs - usually - when testing snaps are piling up with a few days between - it can be read as sign of an upcoming stable snap - and if you look at the Announcements > Stable Updates thread you will get an approximate indicator of when the next stable snap is going to be.
The option to flag a package as outdated makes sense on Arch Linux because they compile packages from source.
I makes no sense on Manjaro because Manjaro repos are synced from Arch repos.
Outdated on Manjaro is a relative term as packages may exist in different versions throughout the branch structure.
If you want a quick view of a give package’s state in Manjaro repo, sync the package manjaro-check-repos. This gives you the mbn utility - which you can use as GUI or from CLI as you prefer.
And the package is up-to-date at the Manjaro Linux extra repo for unstable and testing branch.
But as - already mentioned several times - the main feature of Manjaro is the stable branch - a branch which provides a reasonably stable Linux experience without constantly applying updates..
How you want to use Manjaro is entirely up to you.
If you want to use stable branch - then you just have to wait until the next stable snap.
If you want to change the update frequency - then you switch branch
sudo pacman-mirrors --api --set-branch <branch-name>