The 1948 war, was fought with WW2 surplus on both sides.
Because of the "convoluted" politics at the time (and only the names have been changed to protect the guilty), it was a mash-up on the battlefields. The Israelis received quite a lot of ex-German equipment, from the Soviets, funneled through Czechoslovakia, as it then was. Egypt, Jordan, etc were supplied mainly by the Brits.So, it was not unknown to witness Spitfires dueling with Bf109s (actually Czech-built "Avias"), but with the "Messerschmidt wearing the Star of David and the Spitfires re-badged for an Arab country. Israel managed to acquire a couple of "left-over" B-17 bombers and these "found their way" to the eastern Mediterranean.
As for small arms, substantial quantities of weapons no longer needed by the Wehrmacht arrived, again, often via Czechoslovakia, but having been "collected" by the Red Army. France played a discreet role at this time as well.
What was Stalin up to?
Basically, he wanted to remove both British colonial "influence" AND the increasing US presence from the region. So, if the region could be destabilized by arming BOTH sides, then the place would be ripe for a political realignment. Don't forget that the Nazis put quite a bit of effort into cultivating Arab "nationalism" during WW2. The Mufti of Jerusalem was a regular visitor to Berlin. Hitler wanted access and "influence", the Mufti wanted the usual power and influence, so a deal was struck. Hitlers enthusiasm for killing Jews and his willingness to provide weapons and training were big features. Then, there was the Suez Canal.
When all of that came unglued in 1945, The Mufti and his mates needed a new "patron / strong horse". Who better than Stalin and the Red Army?.
Note that by the time of the death of Stalin (great movie, by the way) the wheels were well in motion. The '56 war was "round 2", by which time, several Arab sates were well down the road to being re-armed by the Soviets, but there was still a lot of the old German surplus on the books. However, the Soviets were moving beyond supplying "used guns" and into industrial-scale developments, particularly in Egypt.
Also remember the other "events" of 1956:
The Soviets were stirring things up in Aden and other places as part of their "de-colonization" programme. Meanwhile, the ruthlessly crushed a civil uprising in Hungary, re-learning some hard lessons in urban warfare in the process. The Hungary "lesson" was the primary operation; Aden was the "diversion". It worked as intended. The parlous state of Brit intelligence services (primarily owned by the Soviets since the 1930s), did not help, either.