I don't think "SharedSupport" is the appropriate place. The legacy documentation says that this location is for "additional non-critical resources that do not impact the ability of the application to run".
Unfortunately, I think the legacy migration documentation is wrong because it explicitly says to use the "Resources" folder for executable code. Don't do that.
Here is the current documentation.
None of that is really what you're asking about, but I think it leads up to it. Typically, launch agents are single-file executables. I'm not familiar with the taskinfo tool or its output. But what it says makes sense. A Launch Agent would run with a user space UI role. That's how Launch Agents work. That's not the same as a Launch Daemon that runs as root and does not require a login session.
When I look at how most other apps handle these things, what you're describing sounds more like a Login Item. A login item would live in "Contents/Library/LoginItems". Of all the apps I have installed that contain items in "Contents/Library", virtually all that contain bundled apps have them as Login Items. So I recommend you treat this thing as a Login Item.
(Note that I mean a newer Service Management Login Item, not the really old school Login Items meant for end users).
It's only recently that Apple added the ability to bundle Launch Agents and Daemons inside an app bundle. In a modern app, I'm not really sure what the difference between a Login Item and a Launch Agent would be. They seem to perform very similar roles. I guess a Launch Agent would be able to use some of the plist config file tricks that a Login Item would probably have to code manually. I can tell you that I have a couple of apps in development that will contain some background functionality and I plan to use Login Items rather than Launch Agents.
