@DeadlyDirk skill up lockpicking ASAP and stock up on lockpicks every time you're at a vendor (they're in frustratingly scant supply in the wild); when you're fully levelled you can start using auto-slots (these regenerate over time) and spending picks to quickly eliminate the unused options, makes it slightly more tolerable but even then it's still a tediously awful, overly time-consuming minigame (and half the time the loot drops from it are a feckin' joke anyway). Genuinely, by the time you get towards end game levels, you're almost better off ignoring anything locked and going with enemy loot drops. And never spend picks to go back steps, if you've messed up a puzzle then back out of it completely as you'll only lose the one pick for retrying the lock completely and the whole puzzle itself will refresh, usually to an easier variant.
Also whilst you're at those vendors pick up as much Adhesive and Titanium as they're selling, they tend to be the resources you run out of quickest when trying to upgrade your gear.
Seriously, out of all the bad stuff in this game, the lockpicking is the thing that can get absolutely **** the most, by the time you get your head around it (and don't worry, you will get your head around it, it's not particularly taxing) you'll see it for the horribly shite game-padding mechanic it is. I don't think a game has ever respected my time less than Starfield, to be honest.