Not really a manager, but managing

My boss, who I work well with over the last few years, acts as more of a "subject matter expert" than a manager. His reports work independendently and come back to him for high level guidance. High level tasks are set by his boss. This suits our type of work (research).

A few months back, a new member joined our team. We all participated in interviews and the consensus including mine was, he was promising, and he was offered and accepted a job. Unfortunately we were mostly remote, so New Guy did not get any of the informal mentoring that usually occurs. My boss asked me to introduce him to one of my projects as part of training, so I had him shadow me a bit. Then our bosses' boss assigned that project to New Guy, so I started a more focused handover. Along the way, my boss asked me to manage New Guy in his tasks, including breaking down the high-level task into shorter term tasks, mentoring him on how to communicate results, etc. Unfortunately, New Guy is struggling both on a technical level, and also on soft skills (getting to meetings on time, regularly reporting back on progress when asked to do so, asking for help from peers without overwhelming them, etc.). It's clear he needs active, daily oversight and a clear definition of each day's tasks, and feedback especially on the soft skills issues. I'd estimate this would be an hour or more of my time daily. I've been doing the daily definition work, and giving my manager feedback on the technical and soft skills shortcomings. My manager independently sees that New Guy is in troubled waters.

Here's my dilemma. I'm just New Guy's peer. If he were my report, I would be doing one on ones and giving him feedback that he's in trouble, though my boss doesn't use those tools. We are on track for a firing without prior "you need to improve" messaging, which seems callous. If he could become a productive team member, everyone's work load would be lightened, most of all mine.

How far should I go in acting like his manager?