Having had from 3 to 14 direct reports the ideal is probably around 7. Too few results is too much attention ("hey boss I have a job to do") while 14 results in total burn out and neglect ("we haven't spoke in weeks - what is your name again").
The latter statement proves the former. A good manager prioritizes management over work that an individual contributor might do. If that doesn't suit a person, they're likely not fit for management.
Tell that to Gartner Group: according to my management they recommend an average of 10 direct reports. They also recommend you don't have "technical managers" just pure managers without technical delivery goals; all that is strictly delegated to individual contributors.
If your management is buying "advise" from the Gartner Group, that is a "bad management smell" IMHO. My advise is to work on your escape plan.
Every time I read or hear Gartner Group "information" piece on a subject that I am competent to judge the value and accuracy of the information, it is at best useless fluff, typically is mostly wrong, and commonly totally wrong.
"An average of 10 reports" goes against the commonly accepted magical number[1] of 7 +/-2. I suppose if the "pure" managers are only pushing paper (unable to judge technical merit), they can support more direct reports. That structure sounds like a recipe for perpetual technical problems.
What you quote sounds like classic matrix management[2] which results in two bosses, one controlling your HR side and one controlling your technical side. That does not work well in my experience because the two managers have very conflicting goals and neither of the goals are in in alignment with your goals. In the ensuing fight, the HR manager always wins because he controls your pay and assignments... and usually is the manager whose goals are least aligned with your goals.[3]
[3] 24 years 9 months in a large corporation with matrix management. It was OK until the Ginormous Enterprise bought the division and sucked all the fun (technical work) out of it.