Does a chair have to be facing a workbench or table to be used there effectively? For instance, if I put a table and a research bench together in an L shape, and I put a chair in the middle, would that work for both eating and researching? Or would it only affect the one it's facing? Do stools work any differently?
It appears that orientation does not matter.
From the Table page on the official wiki:
When placed adjacent to a stool, dining chair, or armchair, colonists will eat their meals at the table.
The way this is worded implies that the orientation of the chair doesn't matter, as long as it is adjacent. The Dining Chair page is similar:
Dining chairs can be placed at tables to allow your colonists to eat there; in front of televisions to let them watch; or in front of production benches to provide comfort as they work...
Usually in Rimworld, if the orientation of an object matters, you'll see an indicator that shows this. For examples:
- All workbenches have the little circle indicator to show where the worker will be working.
- TVs have a rectangular area for where people must be sitting in order to watch.
- Wind Turbines have an area in front and behind them that must be clear of obstructions to generate the most efficient energy.
Since chairs of any kind do not have this indicator, their rotation probably does not matter other than for aesthetics.
Here's the secret truth about workshops -- they don't actually care about chairs. (As opposed to tables, which do, though they don't check for orientation, as per XY's answer)
All that a workshop cares about is the "Comfort" value available on the interaction point. This means that while a chair will "work", insofar that a colonist using the workbench accrues comfort from the object, so will a bed! Or even a sleeping spot! (Which have a > 0 comfort value, for whatever reason).
And, again, since the only thing that matters for workbenches is the "Comfort" value, it is entirely feasible (and space efficient!) to set up workshops where you can have two colonists benefit from a single chair simultaneously!
X - X (Workbenches are Xs) X O X (Colonists stand on O) X - X (- is open space)
In short, orientation does not matter, and "chair-ness" only matters for eating. Anything else is just more Comfort == more better. (And who doesn't like researching from their human leather sleeping bag?)