Hi Larry and welcome to the forums. The main use case for Sushi is as a live-oriented plugin host that routes audio and control data, rather than a full fledged recording studio. As such it doesn’t really have any recording features. It has a rudimentary timeline and tempo that plugins can synchronise with but not much more than that.That said, there is nothing stopping a plugin from implementing its own recording.
Unfortunately Sooperlooper is only standalone under Jack if i’m not mistaken. If it would compile as a plugin then you would be able to run it in Sushi.
edit: Someone already started porting Sooperlooper to a plugin, only took a quick look so don’t know anything about the maturity of the project, but might be worth a shot for you? https://github.com/moddevices/sooperlooper-lv2-plugin