Essentially you are dealing with context-switch overhead and meeting-inefficiency.
An engineer requires time to load the context of their task into working memory (and onto the machine). Each time they context-switch, that investment is lost.
It can take even hours to get "into the zone". And it's infuriating to be interrupted. Unless one is being paid by the hour, in which case they may shrug their shoulders and upstream takes the hit.
If you desire precise numbers, you could perform an experiment. But unless the company is huge, it would be a poor use of energy. It won't tell you anything that you can't deduce from common sense.
Meetings sink focus. Not only is time lost that could have gone somewhere else, but attention is a finite resource. And if 'connection-with-superiors' comes to associate with 'staring-into-space-80%-of-the-time', that's not gona play out well.
Getting to the root of the problem
Use common sense. Observe your own alignment / incentivization and that of others.
Consider the corporate machinery as an extension of the engineering challenge. How can this meta-machine be improved?
toxic ethos / corruption
Consider hypotheticals. What if management is top-down with engineers at the leaf-nodes / bottom-of-the-structure? What if a situation arises where a capable engineer presents a (job-security) threat to their manager/management? The manager experiences a conflict of interest. Self-interest (preservation of role) pushes them to maintain an air gap between their subordinates and their superiors. To encapsulate for the wrong reasons. A corruption occurs.
We're not here to fix the world. We're here to fix ourselves.
The best engineer I ever worked with would constantly say "How can I serve the company best in this moment?". As I learned from this individual and came to adopt this mantra, I started to act as a free radical, applying focus where appropriate. And at some point the work is done, and it is time to journey on. This is as it should be.
If you are contributing (even passively) to a toxic social hierarchy where you consider your 'corporate status' to be greater than those 'below' you, you are now part of the problem.
So the first step is to (re)align your own intentions. Then you are within your own power. "How can I best serve?" may now be applied.
Speak candidly within your sphere. If you are blocked by upper management, can you unblock higher up the chain? If not, could your life-force be better applied elsewhere?
Use common sense. Be a facilitator. Let those around you know it. Invite discussion. Humility wins.
Using Slack/Discord/... allows async contributions. Team members contribute when they have bandwidth. But constant notifications reduce productivity.
One practice I've enforced is that each team-member leaves a daily update at the end of their working day in an #updates channel.
- What they did
- Any issues outstanding
- What their immediate TODO list looks like
Then as coordinator I need to start work a little early and keep on top of that.
If I have to solve a problem that requires 3 team-leaders, sometimes it's best to go to each one individually, gather all information, figure out solution, then make a temporary channel on Slack/Discord, dump the info, ask for feedback or a 👍. Once I've got 3 👍s it's actionable, with minimal disruption. Nobody's spending a moment staring into space while some meeting discusses something not relevant to them. And, unless it was urgent, everyone responded in their own time, so context-switch disruption was minimized.
Companies that promote developers to managers tend to experience a win, as then the manager naturally understands the constraints of the developers. Most meetings emerge from needs of technical teams to joint-solve issues. A meeting is often a "last resort".
If you're a manager without a s/w dev background, you just need to apply common sense.