Are projects deleted after a certain time? Can I archive them?

No. Projects aren’t deleted when left inactive, nor do they expire. They stay in your account for as long as you keep them.

There’s no separate archive function. A project stays exactly where it is until you delete it or wipe its data.

To reduce clutter instead, set up an automation with the Hide source keys action to keep specific entries, like brand names, out of the translation workflow, or switch the project to Private or Secret in project settings so only invited members can see it.