Actually salvaging:
In 90% of cases, if I don't salvage something it's because it would be too tedious to do/not worth my time. From there there's about 9% where I don't have room to do it right (orbital station usually), and then finally there's the 1% of times where I can't because of enemies.
Further the actual process is "click through the menus, grab everything, control click on fuel/metals if i go over the limit".
In short, there's next to no thought put into it, it's just me mashing through menus.
Economy:
The other issue I find with salvaging is that you just hoard all of it. Yeah you could sell weapons/ships, but it's not worth it (in part because of how frequently/easily you can salvage them), so you wind up with an apocalyptic supply of weapons sitting in Corvus or one of your planets inventories.
So looking at this, the 3 main payoffs to a salvage that actually get my attention are:
1. Blueprints
2. Recover a hard to acquire ship
3. Ship systems (fast missile racks, ITU, whatever).
and then misc (usually a nanoforge/core or a relevant amount of trade goods, which is just money). notice that i've NEVER not salvaged because I was worried about losing machinery or crew.
1 and 3 matter less and less the longer the game goes on. Usually by the time i'm ready to start up some colonies i've already got 70-90% of the blueprints in the game. I'm the ultimate hodgepodge empire before I've even started, or can theme however I want. There's no "hunt" for blueprints, or any real strategy to it. Just play the game, you'll get them. Ditto on ship systems (add check out the markets for this one, it takes a very short amount of time to get most of them).
So what was once an interesting moment of salvaging a ruin or battlefield quickly becomes done for the sole purpose of "i need supplies/fuel" or the rare case when you see a legion floating in space.
Some possible solutions:
1. Make salvaging take time/more costs:
Maybe not EVERY salvage (post battle shouldn't for example) but when i come across ruins/orbital relays/shipwrecks maybe it should be done the same was as a comm sniffer install used to. This would lead to many more situations where you can't salvage because of enemy threats, and allows skills/systems to modify it.
2. Change ship/weapon drop rates:
I think ships should be much more likely to not be salvageable at all. The "Default" method to acquire a ship ought to be through the marketplace (and i have another topic i might do on the black market), not salvaging post battle. This would allow an economy tweak to where selling a salvaged ship is now worth your time and yet another way to have salvage skills matter more. This should be similar with weapons (maybe by complexity level) so you don't leave on a bounty hunt and come back 7 tech levels ahead of when you left from combat and incidental exploration.
As a side effect this could lead to cheaper restoring. Right now it's hyper expensive because it's pretty easy to wind up with a hanger full of d-modded hammerheads, so price is the only thing stopping you. If that situation was actually rare you don't need restorations to always cost so much because there's other factors stopping the player.
3. Give it real costs:
Even if you don't add time to a salvage, losing a few crew and some machinery is a joke. Machinery should NOT be so common from a salvage as it just feeds the infinite "oh look salvage is free" loop, but exploring that research station at the edge of a black hole while in emergency burn ought to come with threats to your CR at the very least (outside of the eburn).
4. Give resources more of a meaning-
This is a large one so i left it for last as it might be out of scope, but right now the only difference between metals and organs is the market price. At the very least going into mid/end game it might be more interesting if constructing your own ships actually required resources, so I can look at an incidental amount of plutonics as maybe helping me build my own fresh Medusa rather than spare change that I have to click on more. There's some precedent in building nav relays/machinery for salvage/using the neutrino detector, but I think giving all the various trade goods more of a gameplay use would help the salvage system matter more. Maybe i'll think more about if i want to dump my metal for food if it can be turned into more heavy machinery that I need for X or Y reason.
Alternatively to all this, if salvage isn't meant to get much deeper, maybe it should take fewer clicks? A "store/take all weapons" button would be nice at the very least.