At what employee count is a company “too big”?

It would be too generic and naive of me if I mention a magic number. It all depends on the structure of the organisation. The company could be over 100,000 people but most of the employees might work/interact with only a handful group of people daily or a company might be less than 100 people and you might need to go through half of the company to get one thing done.

There are some logical conclusions you can make. For example when the hierarchy goes long and sharp on the tip it is very likely that a re-organisation/being flexible is going to be painful.

From my experience the slimmer and taller the pyramid it will be more top to bottom execution with no negotiation hence less flexible but to an extend agile (all pressure on bottom row) which is the least favorite place for people with ideas and creativity to grow.

I've worked in 30-40 employee companies completely bogged down in inflexiblility and 10000 employee companies where I had all the flexibility and agility I could ever want.

Employee count is probably one of the least indicative indicators of how lean, agile, flexible, etc. a company is.