Voadam
Legend
The rules do not go down to that level of specificity so it is a ruling situation.I'd be inclined to agree..logically.
That said, I've never found anything that says that manacles (or any other equipment) actually prevent the use of your hands.
Binding a hand to something seems reasonable to me to say makes the hand not free.
I don't really see much of a basis for knock on effects for thieves tools from ruling on whether manacles prevent somatic components.(And there are some interesting knock-on effects if we say that they do, like how a rogue could pick a set of manacles without having the free use of one of their hands)
Again I do not think this level of specificity exists in the rules, so whether a manacled rogue can physically access the lock to pick the lock on their wrist manacles while bound seems a DM call based on the situation, not a categorical rules situation that applies universally to spellcasting somatic components and thieves' tool usage.
Manacled and stretched out on a rack seems harder for a rogue to self pick than if the manacles are just attached by a two foot section of chains. I can see a DM ruling a tightly cuffed rogue cannot access the lock, or saying go for it Houdini with your palmed hairpin.
The somatic components description does specify free use of a hand so that is what we have to go on as a starting basis for a ruling.
Lockpicking is not specified but it is a real world and cinematic thing to do so a DM call based on that kind of a view seems the starting point for a DM ruling.