I believe that – and please forgive me if I am babbling – that you have to keep your target audience in mind. This will drive some aspects of where you want to position this option.
Me, a hobby photographer with a 20odd MPx Nikon DSLR, running a small website, accustomed to desktop class photo editing tools, very familiar with LR and A3, some experience in Capture one, familiar with Luminar and On1 and similar, appreciating and embracing an iPad-centric (potential) workflow:
I would like to see this export option in the edit UI.
The “done” option commits to all the changes I made – it resembles the good ol’ “save” button. Very little control and a predetermined action. This option is currently located in the edit UI.
There could be, on the same level, an “export” option. This action will open a more sophisticated sub-screen which lets the user decide things like the file name and the storage location. Positioning the button there allows me to implement a “version workflow” on the iPad (apologies for being a dinosaur). Affinity went down the tradition desktop UI route on this one. And I believe, considering their audience, that that’s totally acceptable and suits the user base just fine.
Making it part of the share sheet in the “done UI” would imply a secondary menu so I can choose share (export) options – but only in case I choose a location which requires this kind of user input. It would also require me to fully commit to edits (done) before being able to “share” or export. Please keep in mind that this way of hierarchy thinking comes from a Dinosaur 🙂
I am not sure wether iOS allows you to have a share sheet Icon on either leve, the edit-UI and the done-UI. And I also don’t know how you could adjust the share options in either UI, so that when sharing in the “edit” section the share sheet would only allow for certain share levels (e.g. files) whereas sharing on the “done” leve focuses on other share levels (such as Twitter, FB etc). As you mentioned in you post, sharing it as TIFF from the browsing level would imply the app having to download a JPG, converting it to TIFF and sharing it as such. That can add more confusion than benefit.
As far as device, you will know best who downloads on what device and therefore where you need to focus.
The only reason I downloaded RAW power on the phone was that my old iPad 4th gen did not support this software and I really wanted to check it out. My iPhone 6s was my only option. As with any other photo software I came to the conclusion that using the phone other than for capture is only suitable in case of extreme emergencies.