Due to various internal reorgs my manager currently has a number of reports approaching that number. It's mostly gone fine for now, because there are multiple teams under her that are mostly self-sufficient in deciding their product direction. We have a team lead who isn't a "manager" but is providing input on what we do and we go to her when we have problems or need administrative work done. It's not horrible.
Your manager’s manager should be working with her to help her address the issue, because it’s not sustainable. It may be okay for now, not disputing that at all, but what to you may look like relative calm is much more likely her giving her best imitation of a duck (calm on the surface, but paddling furiously).
For instance, has she had to reduce the frequency, duration, and/or quality of her 1:1s? I’m guessing the answer is “of course” and maybe some ameliorating fact like having more 1:1 time with the team lead. The “so what?” here is that 1:1s are how you head off problems before they get serious. So either the tech lead is picking up that slack and is your de facto manager or you’re simply coasting on the strength of past 1:1s, but inertia will only get you so far.
Also, this tech lead you mention is likely doing less actual technical work because they are picking up slack left by your manager not having enough time in the day. This might not be a problem right now, but the first question I would be asking in your manager’s shoes is: “is my TL happy? Is this sustainable for them?” The second would be something like “What long term technical objectives are being sacrificed to deal with this management issue?”
It’s often the case in the situation you’re describing that the TL is interested in moving into management, and this is a “try out” effectively. Personally I like to be open about situations like this, although there are valid arguments against that. In any event, I think most people would agree that it’s best do such “try outs” when the stakes are relatively low, and the TL can have an easy escape if they need it. The situation you’re describing doesn’t fit my definition of low risk, although ymmv — maybe conditions are such that this is a very temporary state and the machinery to fix it is already in motion.
> It’s often the case in the situation you’re describing that the TL is interested in moving into management, and this is a “try out” effectively. Personally I like to be open about situations like this, although there are valid arguments against that. In any event, I think most people would agree that it’s best do such “try outs” when the stakes are relatively low, and the TL can have an easy escape if they need it.
The best way I’ve seen to accomplish this is have a job title that’s purposefully ambiguous. Usually I’ve seen this as a “lead engineer”, which can come with or without direct reports. This lets people try out management while giving them space to change their mind without losing title or status.