Pat the salmon fillets dry with paper towels and season all sides generously with salt. Set aside.
Add the wine, vinegar and shallot to a small saucepan and set over medium-low heat. Bring to a simmer and allow to reduce until only a couple of tablespoons of liquid remain, about 3-5 minutes.
Once the wine mixture has reduced, add a piece of butter and whisk constantly to melt it into the mixture. Once melted, add another piece and repeat. Continue this until all of the butter is added and the sauce is emulsified. Remove from the heat and set aside.
Set a large skillet (preferably non-stick) over medium-high heat and add 2 tbsp of neutral oil. Once shimmering, add the salmon skin-side down. Cook until the skin is deeply browned and the fish registers 40°C/104°F on an instant-read thermometer - about 5-7 minutes. Flip & cook on the other side until the interior is 50°C/122°F. Remove from the pan and allow to rest, skin-side up, while you finish the sauce.
Return the sauce to low heat and whisk constantly to heat it up again. Whisk in the capers and the lemon juice. Taste to adjust for seasoning, adding salt and pepper if needed.
Remove from the heat and spoon the sauce onto a plate. Place the salmon, skin-side up, on top of the sauce. Serve immediately.
Notes
I like the complexity of sherry vinegar, but feel free to use white wine vinegar, red wine vinegar or even apple cider vinegar if that's what you have.