Contain
One permission, one drag to Applications, and nothing else.
Requirements
You can grant or check the permission any time under System Settings → Privacy & Security → Accessibility (add Contain with + if it is not listed). Contain's own Settings tells you whether it is still in place.
Installing
Contain is signed and notarized by Apple, so it opens like any other app — no warning to click past, no workaround needed. Open the disk image, drag Contain to your Applications folder, and that is the whole install. It keeps itself up to date from there; the download page walks you through it.
You will not find it on the Mac App Store. Apps there run walled off from the rest of the system in a way that blocks the one thing Contain does — moving another app's windows — so a store version simply would not work. We publish it directly instead, and always sign it the same way, so an update never costs you the permission you already granted.
It is on Setapp, though. Get it there and the Setapp app installs Contain and keeps it up to date, with no key to paste in; it is the same app and asks for the same permission. macOS counts the two copies as different apps, so if you move from one to the other, it asks for that permission once more.
Granting Accessibility is what lets Contain move a window at all — a handful of things still behave differently to what you might expect, and those are set out on Limitations. What does and does not leave your Mac is in the privacy policy.
€6 once · 3 Macs
One price, no subscription, no account. Download it, paste in a key, and the windows you already have open become tabs in a single window.