There is basically no overlap with Amdahl's law here. Amdahl's law just says that there are diminishing returns on the whole when increasing parallelization in a program with significant serial parts. It is a fairly obvious observation, but people seem to distort it and apply it to general scalability.

First, everything needs to be synchronized but that doesn't mean synchronization is expensive or blocks computation from happening. Lots of synchronization isn't even dealt with explicitly by users, it happens in queues in the kernel, in networking hardware, or even in the memory controller when talking about reading from memory.

The closest thing is the database becoming a bottleneck, but that is not because of Amdahl's law or even synchronization, it just about reads, and those are extremely parallel, so it likely comes down to total CPU power when it is a problem. That's why query caching can be so effective - it isn't about synchronization and definitely not about serial parts of a program, it is just about usage.

For connected social media sites, not everything has to be done on a page request. Anything done ahead of time is also done in parallel.