As someone who lacks the skills to program and wouldn't be doing the programming work, I was just trying to be respectful of your time (and the team's time) since I've got no clue what work would be involved in implementing any of the options.
But since you asked, here goes:
I'd add a menu item called "Summarize Page" to the Favicon menu. I'd put it below "Find on Page."
Clicking the menu item would open the URL https://kagi.com/summarizer/index.html?url=[current URL]
If the Orion user is a Kagi subscriber, they'll get the summary.
If the user does not have a Kagi account, they'll see the page that Universal Summarizer already generates if someone who does not have a Kagi account tries to use it (this is a screen shot of what I see in the Chrome browser on my iPhone, where I'm not logged into my Kagi account).

I'm not sure what the percentage of Orion iOS/iPadOS users is who do not have a Kagi account, but it seems to me that this screen would be good at introducing such users to Kagi and the summarizer, potentially creating new users. (I'm assuming that's why the red text and link to Kagi Search already appears there). That seems a net positive to me. But if you're concerned that having a feature in Orion that only works for Kagi subscribers would be a turn off to some Orion users, you could also add an option in Settings -- I'd put it under Search Engine Suggestions -- that gives the option to Show or Hide the Summarize Page menu option.