You do not need to upload photos. If you have these apps installed on your phone and you grant access to the photo library, they already scan for CSAM. These apps aggressively upload some contents in the gallery to speed up the upload process when you make a new post. That's why Apple implemented access to the gallery on a per photo basis.
According to the FAQ:
Does this mean Apple is going to scan all the photos stored on my iPhone?
No. By design, this feature only applies to photos that the user chooses to upload to iCloud Photos, and even then Apple only learns about accounts that are storing collections of known CSAM images, and only the images that match to known CSAM. The system does not work for users who have iCloud Photos disabled. This feature does not work on your private iPhone photo library on the device.
Does turning off iCloud Photos disable CSAM detection?
Yes. When iCloud Photos is deactivated, no images are processed. CSAM detection is applied only as part of the process for storing images in iCloud Photos.
I also don't see any references to what you mention in the technical implementation document, though I think you might be referring to this:
Before an image is stored in iCloud Photos, an on-device matching process is performed for that image against the database of known CSAM hashes. This matching process is powered by a cryptographic technology called private set intersection, which determines whether there is a match without revealing the result. The device creates a cryptographic safety voucher that encodes the match result. It also encrypts the image’s NeuralHash and a visual derivative. This voucher is uploaded to iCloud Photos along with the image.
which wouldn't happen unless iCloud Photos is enabled, after which the comparison is made prior to the upload.