Moving your saved statuses to a new phone
Saved statuses are ordinary files, which makes this simpler than people expect — and unrelated to your WhatsApp backup.
Good news first: once you have saved a status, it is an ordinary photo or video on your phone. Moving it is the same job as moving any other file, and nothing about WhatsApp is involved.
Why your WhatsApp backup does not cover this
A WhatsApp backup contains chats and the media inside them. It does not contain statuses — neither the temporary files in the statuses folder nor the copies you saved out of it.
So restoring WhatsApp on a new phone brings your conversations and brings back nothing you saved from a status. People discover this at exactly the wrong moment.
Where your saved files actually are
Wherever the saving app wrote them — typically a folder under Pictures, Downloads, or an app-named album. They are visible in your gallery, which means every normal transfer method already handles them.
Methods that work
Google Photos, if you have backup enabled and the save folder is included in the backed-up set. Check that: device folders are often excluded by default, and "backed up" for your camera roll does not imply backed up for an app folder.
Phone-to-phone transfer during setup — Samsung Smart Switch, Google's own transfer, or the manufacturer's tool. These copy the filesystem and pick up app folders.
A cable and a computer. Unfashionable and completely reliable. Copy the folder, paste it on the new phone.
Cloud storage — Drive, Dropbox, whatever you use. Upload the folder, download on the other side.
Before you wipe the old phone
Check the save folder explicitly rather than assuming the transfer caught it. Open it on the new device and count. App-specific folders are the most common thing a migration silently skips, precisely because they are not the camera roll.
What cannot be moved
Statuses you never saved. If it was still sitting in WhatsApp's own statuses folder, it expired at 24 hours and is gone on both phones — the old device does not hold a copy either.
Which is the recurring lesson of this whole subject: the save is the backup.