Should I be able to view .cr3 Raw files in the iOS file viewer rather than the photos app?

Given your stated workflow, you might consider using a third-party App that is better suited to the task. Your hardware arrangement can be similarly optimised.

Consider Stratopherix FileBrowser - Document Manager, or its “pro version” FileBrowser Professional:

https://apps.apple.com/gb/app/filebrowser-document-manager/id364738545

https://apps.apple.com/gb/app/filebrowser-document-manager/id364738545

FileBrowser will permit you to directly move images from SD to SSD. FileBrowser supports a wider range of image and RAW camera formats. The App is regularly updated by the App Developers to include newer RAW formats.

When using FileBrowser, images can be viewed and assessed for “culling” in-place - without having to first copy the images to the iPad for viewing or editing.

You might review the extensive online Manual and help files to determine suitability for your needs.

https://www.stratospherix.com/products/filebrowserprofessional/filebrowser-professional-user-guide.php

You will of course require an appropriate/compatible USB hub to permit simultaneous connection of both an SD Card reader and SSD - although some USB hubs include an SD/mircoSD card reader amongst their compliment of additional ports. Assuming that your iPad has a USB-C port, I suggest (and recommend) the Kingston Nucleum hub - this being known to be fully compatible with iPad Pro.

https://www.kingston.com/unitedkingdom/en/memory-card-readers/nucleum-usb-type-c-hub

Speaking of personal experience, sometimes needing to perform similar file/photo management to yourself, an iPad Pro 12.9” M1 paired a Nucleum hub has performed well, although with microSD cards I can achieve higher read-performance when using a USB3 Type-A microSD card reader connected to the hub. By example:

https://www.cameramemoryspeed.com/reviews/card-readers/lexar-lrwm03u-7000-uhs-i/

The USB SSD can be simultaneously connected to the hub using another USB3 Type-A or USB-C port.

The Nucleum also supports USB PD passthrough, allowing additional connection of a USB PD Power Adapter of at least 20W (30W or greater recommended).

I don’t know which camera uses cr3. Here are the supported RAW formats: Digital camera RAW formats supported by iOS 15, iPadOS 15, and macOS Monterey - Apple Support

Here’s the in-built supported image format list: Loading Images