The IAI Searcher drone deal is more an exception than the rule. There was general thawing out between Russia and the west, and that was part of an attempt to shift things into more friendly territory but it never progressed beyond that one deal which was for equipment considered obsolete by Israel anyway.
Except... it wasn't just the one deal. Elbit camped out by the Ural Civil Aviation Plant for years. And this was after relations started to get frosty with Europe again. Iirc the US even got upset that Israel was allegedly supplying US tech to Russia in violation of sanctions. And this is just the part we can see. There were other... maneuvers. There's a reason Israel wouldn't sell UAVs to Ukraine even post 2014. Let me ask you this,
when did Elbit stop cooperation on the Forpost-RU and the family of UCAV munitions being integrated on it?
Israel and Russia has a relationship behind the scenes. They're not exactly allies, and it's probably an uneasy partnership at best. But they're definitely not enemies. Not based on their mutual behavior. They're on different sides of the current global cleavage but Israel will sell upgraded pitchforks to hell itself if it's in their interest to do so.
Plenty of things were different before the war and Russia was just another client. The French sold thermals that were used for Russian tanks (Thales (Catherine-FC) / JSC Peleng) for example. Eyebrows were raised but the deals went ahead.
France was selling Russia warships and iirc the SENIT 9. Russia actually had good relations with France even after the events of '14. This current war of course tossed all that out the window, yet
another reason for why it was a bad idea to invade. But I digress.
On a side note, you said "before the war". But which war to do you mean? The current one that started in 2022? Or the one '14-'16? The timeline here shows a fairly substantial difference. Russian defense cooperation with Italy and France was winding down post Crimea. But the Forpost-RU is all after that.
What is relevant is the current context. Russia was in Syria and supported Assad for its own self serving strategic interests (access to a warm water port on the Med, airbases to support operations in Africa, skin in the game to influence geopolitics in ME), not for any great love for the man himself.
Sure and in this regard Russia is different to every other player in the region who do it for the love of the men they support. Especially the US with their support of the Syrian Kurds. Russia supported Assad because Russia was very short on client states and Assad's Syria was one of the last few remaining. If Assad had managed to reclaim Syria's oil wealth, it would have been a boon to Russia as he would have spent that wealth on Russian rail infrastructure, and military hardware, and whatever else Russia was keen to export, presumably a bunch of Ladas and Ural trucks (though the Syrians were for some reason partial to the GAZ). Russia also supported Assad because there was no other viable option for the Mediterranean base. Libya was a total mess, and everyone else politely said no including Algeria. In other words the current defeat isn't that bad for Russia if they can keep the bases. They might even profit from this if the new Islamist Syria gets control of the oil wealth and wants to shop for weapons while being sanctioned by every civilized country for the usual reasons.
Would Israel be happy if Russia exits? I'm sure they will be. While Russia is not a direct enemy of Israel, one less variable and player in the region is better since it is one less consideration.
It depends on what else accompanies Russia's exit. I suspect all things being equal Israel might prefer Russian bases not to be there.