Imagine no POD earlier than 1945, with such a regime in place and established by about 1965 at the latest. It isn't, for the record, necessarily a regime that is going to last a long time either. But let's say it will be extant, and a thorn in Washington's side, for a minimum of 2 and a half years (through whatever combination of good strategy and sheer luck on the part of the leadership in Panama City and their buds in Moscow).
What does "pro-Soviet" mean? It doesn't necessarily mean that Panama is ruled by an explicitly Marxist-Leninist party, or that Panama has publicly gone so far towards the Second World that it isn't a part of the Non-Aligned Movement. What it does mean is that the government in Panama City is actively collaborating with the Soviet Union in a way that is beneficial to that superpower and harmful to the interests of the United States. This is much more than the local dictator's son getting to study in Moscow, in other words. There is actually some high-level political intrigue warranting at least some level of espionage, military positioning, etc. And probably involving access to the Panama Canal because, well, obviously.
In this situation, I imagine that the Panama Canal would not actually be nationalized - unless the United States is really having a lot of trouble, which probably things are going poorly elsewhere in the Cold War. But who knows. I imagine that there will be effects for Panama's neighbours, especially Costa Rica, which I think had a fairly social-democratish presidency for a lot of the Cold War, but managed to get left alone in comparison to its neighbours. This might change that? Finally, I guess it matters a great deal whether a Communist-led Cuba exists in this timeline or not, but if it did, I imagine that a friendly country nearby would probably be very helpful for the project of spreading socialism around Latin America. But, hey, maybe without the Panama Canal, it's simply not that useful.
What does "pro-Soviet" mean? It doesn't necessarily mean that Panama is ruled by an explicitly Marxist-Leninist party, or that Panama has publicly gone so far towards the Second World that it isn't a part of the Non-Aligned Movement. What it does mean is that the government in Panama City is actively collaborating with the Soviet Union in a way that is beneficial to that superpower and harmful to the interests of the United States. This is much more than the local dictator's son getting to study in Moscow, in other words. There is actually some high-level political intrigue warranting at least some level of espionage, military positioning, etc. And probably involving access to the Panama Canal because, well, obviously.
In this situation, I imagine that the Panama Canal would not actually be nationalized - unless the United States is really having a lot of trouble, which probably things are going poorly elsewhere in the Cold War. But who knows. I imagine that there will be effects for Panama's neighbours, especially Costa Rica, which I think had a fairly social-democratish presidency for a lot of the Cold War, but managed to get left alone in comparison to its neighbours. This might change that? Finally, I guess it matters a great deal whether a Communist-led Cuba exists in this timeline or not, but if it did, I imagine that a friendly country nearby would probably be very helpful for the project of spreading socialism around Latin America. But, hey, maybe without the Panama Canal, it's simply not that useful.