I would argue that this has more to do with the way that TCP works, and not with OpenVPN per se. Here comes a long rant and my few cents:
Is my understanding correct?
Roughly yes, but the inner TCP connection isn't "protected". If the outer drops a packet and the throughput gets lower or latency higher, the inner connection would also be limited by this, notice that it can't use full performance and start to back off.
It seems that the TCP-over-TCP meltdown is only internal (i.e., it only affects local buffers) but does it also affect the network as well?
You will only have one TCP connection to the server, so this will only affect that particular connection and whatever is in it. What the meltdown refers to is what I describe in the previous answer.
Does it cause more congestions in the network and does it degrade other connections on the same network?
No, but I would need to have "network" being defined here. If you have a bad connection to the Internet, then yes, all would suffers from packet drops or other transmission problems. If you mean there is only a problem with your client<=>server connection, then your non-VPN connections wouldn't be affected.
How does TCP-based VPNs solve this problem?
By using a single connection to the server, send the traffic inside that connection and hope for the best.
OpenVPN has an article on this but it does not say why it is not a problem in practice, is it a problem in practice.
Yes. TCP has much higher overhead in terms of packet size than UDP, so you are always paying a size penalty by having two TCP headers (inner plus outer) in your connection. Resends and TCP rampup will also impact your performance. If you have a good connection, i.e. no drops, low latency and high bandwidth, then you won't see much of the rampup/backoff/resends, and hence not notice this. If you have a bad connection, then the first answer comes in to play, the outer connections could ramp down, this will impact the inside traffic which will ramp down, packets can become out of order and being resent and so on, which will definitely impact the tunnel performance.
Long answer is long. I hope this made some sense to someone more than me.