With the likely exception of the Inchon landings I can't think of any post ww2 US operations that involved divisional sized combat operations without host nation support. (Maybe the 1958 Lebanon operations and the later operations in the Domican republic also come close ?)
Not even sure I would count the Inchon landings given that the US had Japan as a staging base and the Pusan Pocket in southern Korea to provide some amount of support in terms of air cover for the landings.
In any event if one assumes a friendly host nation that allows for a peacefull off load in a port and provides a reasonable amount of host nation support then nations such as Canada for example could on paper at least have deployed brigade groups with tanks, self propelled artillery and APC's overseas during the Cold War. I don't think this is quite the type of answer the OP is looking for however.
The ability to actually land forces in the face of opposition and sustain them during combat without a near by friendly port is what sets super powers apart from nations such as Canada IMHO
Well actually your description of Canada sounds very much in line with what the OP was looking for.
Look back on the the OP and we see:
"Goal is to provide some support for their allies in localized conflicts like
Angola civil war
Libya vs Egypt late 70s
South yemen
Horn of africa
Prevent coups against friendly regimes"
In none of those examples would it be a case of Soviet forces needing to be landed in the face of opposition/combat and indeed what the OP was asking about seems like what your standard expeditionary force (whether it be American, BEF, Canadian, Australian, New Zealander, South African, Indian, French, Brazilian or Cuban (to Angola), ) would be expected to do.
The requirement that such a force needs to be landed in the face of an opposing force is, as noted before, not the usual historical experience of expeditionary forces especially after 1900 (the various amphibious landings in the World Wars being the bulk of instances where such landings were opposed). And more often than not the landings were with host nation support or it opposed they were opposed by forces noticeably inferior in numbers, experience, organization's or armaments or some combination of such (eg Grenada). Again the opposed landings in the World Wars (a period of 10 years out of the entire century) was the period where this wasn't the case. So in essence what you have been asking for is something very different from the OP - the ability of the Soviet Union to conduct opposed landings in a World War type situation, not just to help allies in localized conflicts.
The Falklands example is the only other one besides Grenada that I can think of with opposed landings and combat (I don't think even Lebanon in 1985 counts as there was some kind of local acquiescence at least by some factions in Lebanon).
But then that's still quite different from the OP as the UK wasn't landing forces to support an ally in a localized conflict but was landing forces in a straight up conflict over British territory (and even here the Falklands population was entirely pro-British so even though the Argentine military forces opposed the British, any British force that landed on the islands would quickly receive local support which would be invaluable). The USSR didn't have overseas colonial territories so this kind of fight would simply just not occur
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