Can iMessage send a video as-is, without converting it first? If I share a video file via iMessage, the recipient doesn't get the exact file I've shared, but a converted version of the video, which has a lower resolution and lower quality (e.g. when I share a 1080p H.265 video, iMessage actually sends a 300p H.264 blurry mess.)
Is there a way to make iMessage share a video without re-encoding it? What are the technical criteria that video files have to meet in order to be spared re-encoding? (codecs, profiles, resolution, file size)
I know I could share a URL to a file hosted elsewhere, but I want to have end-to-end encryption, and I don't want to require the recipient to perform any unusual steps or leave iMessage to view the video.
I don’t think we get to directly influence this.
For my threat model, I’m not super concerned if iCloud and Apple can decrypt the attachments stored in iCloud, so I typically save the video to iCloud shared photo album and share a link. If you’re sharing copyright content or something you don’t wish the government to get at via a cell carrier I understand not wanting to upload that to a server.

https://support.apple.com/en-us/HT204042
https://support.apple.com/guide/security/imessage-overview-secd9764312f/web

Also, be sure your carrier settings are updated, some carriers influenced sending quality in the past, but I haven’t seen that happen lately in the US.
The function of iCloud and Messages/FaceTime varies greatly based on what region your device was sold and what region you associate your AppleID. Even in the US, Apple may upload the content of your messages to their servers, E2E encryption may not be compromised substantially when you are sending large attachments.

https://support.apple.com/en-us/HT209110

If you need end-to-end encryption, letting the video be compressed might be the lesser of two evils.