How to verify the original date of a photo transferred from an old iPhone to a new one?

Culd you please elaborate a bit on the on the media kind you are asking about? Your question contains contradictory information.

In the tile of your question you wrote "verify the original date of a photo " but in the body of your question you are asking about a video: "now I’m trying to find an old video". That is a very important difference, because there is an exif standard for the capture dates of photos set by a camera, but not for videos. Some videos cameras are embedding the capture date in the original filename of a video, and others are taking a photo as a sidecar file, where the capture date is saved in the photo taken hat the same time. If there is no sidecar file and the filename does not include the capture date, you may want to inspect the file creation date of the original image file.

And are you using iCloud Photos to sync the photos and videos between your devices? The syncing with iCloud does not always preserve the original file creation dates, when we download the original image files from iCloud, but it will (mostly) preserve the original fileaname. You may get an idea of the capture time of a video, when you compare the filenames original image taken at the same location to the filename of the video in question. If you have a video with the name "IMG_6362.MOV" and photos with the name "IMG_6361.HEIC", and "IMG_6363.HEIC" you will know, that the video has been taken in the interval between the capture dates of "IMG_6361.HEIC" and "IMG_6363.HEIC". that ill narrow down the the range when the video has been taken.

Apple used to preserve the original image files in the photo library exactly as they have been added to Photos, but that has changed with iOS 12 and macOS 10.10.14 Mojave, when Apple replaced the files in iCloud by uniquely named copies. And when we are syncing several devices with iCloud Photos and there are duplicates between the devices with contradictory metadata, only one version is kept.

Your best bet to find the original capture date would be to look at a backup copy of your video or photo that you saved directly before importing the item to Photos. are you saving backup copies of your photos and videos on a computer?

Photo metadata, particularly the date and time a photo or video was captured on an iPhone, depends on several factors. The information displayed in the Photos app can be influenced by the device used to capture the image and how the file was subsequently transferred, shared, downloaded, or saved.

Several factors can affect photo metadata:

1. Original device: Was the photo taken using your iPhone, another iPhone, or a different camera?
2. Third-party cloud services: Was the photo uploaded to a third-party cloud service and subsequently downloaded? Depending on the service and download method, some metadata may be preserved, modified, or stripped.
3. Transfer between devices: Was the photo transferred to another device and then transferred back to your iPhone? The method used can affect the metadata.
4. AirDrop: Was the photo received through AirDrop? AirDrop generally preserves the original file's metadata when the original photo is shared, although the outcome may differ if the image was edited or converted.
5. Email: Was the photo emailed to you and then saved to your Photos library? The result depends on whether the original file was sent as an attachment or the image was resized, converted, or embedded in the email.
6. Shared Albums: Was the photo shared through an iCloud Shared Album and subsequently saved to your personal Photos library? Shared Albums may deliver reduced-resolution images without all the original metadata.
7. Windows PC: Was the photo transferred to a Windows computer and then copied back to your iPhone? Copying the original file generally preserves its metadata, but certain applications and transfer methods may alter or remove it.
8. Screenshots and editing: Was the image a screenshot, or was it edited, exported, or converted using another application? These processes can create a new file with different metadata.

Why is the Info (ⓘ) button important?

When you open a photo or video in the iPhone Photos app and tap the Info (ⓘ) button, the information displayed provides valuable clues about the image's origin and characteristics.

Depending on the available metadata, you may see the date and time, camera model, lens information, geographical location, image dimensions, and an indication that the image is a screenshot.

This information helps establish what is known about the image, although it does not necessarily reveal its complete transfer history.

What do "No Camera Info" and "No Lens Info" mean?

1. No Lens Info: This means the Photos app does not have lens information available for display. It does not, by itself, prove that the photo was transferred from another device or that its metadata was lost.

2. No Camera Info: This indicates that the relevant camera information is unavailable. Possible explanations include missing metadata, an image generated or processed by another application, or a file that does not contain the expected camera information.

3. Screenshot: A screenshot is generated by the operating system rather than captured through the iPhone's camera. Therefore, it should not be expected to contain the same camera and lens information as an actual photograph.

4. Lens information is available: If lens information appears, it indicates that the relevant information is available to the Photos app. However, it does not conclusively prove that the photo was taken using your current iPhone. It could have been captured using another iPhone or camera.

The bottom line

The Info (ⓘ) panel is an important starting point for understanding a photo's metadata, but its contents must be interpreted in context.

The presence or absence of camera and lens information can provide useful clues, but it cannot independently establish the complete history of a photograph or prove that metadata was lost during a transfer.

To understand what happened to a particular photo, consider its available metadata, original source, and transfer method.

As léonie says, videos are especially vulnerable, because there are way fewer (and in the past way, way fewer) standards for recording and preserving metadata. Many of us keep separate back up copies of our original picture files. Especially with a new phones like yours, the USBc port makes it really easy to just plug in an external disk drive (no extra computer involved), select pictures, and use Share>Export Unmodified Originals to make a copy of your pictures and videos that will be universally accessible, and which won't change with upgraded OSs or fluid codecs.

Alternatively you can do this

Transfer photos and videos from your iPhone or iPad to your Mac or PC

Frankly, for backing up originals, the "plug in a hard drive" method uses fewer parts, and it may make more reliable copies. Then again, using two different methods is a good idea.