I don't have any chars near timber right now to check but I believe it tells you when you start a new project from the location screen that timber can only be gathered using a tool and lists the tools you can use.
Similar to the screen for stone but without the manual rate:
Note that in one day one person can only dig 750 gram. The number of turns will be rounded upwards. The end result will have a random deviation (max 20%) of the amount you ask for.
If you have pickaxe, you can dig 1500 grams a day.
If you have bronze pickaxe, you can dig 1500 grams a day.
I'm not sure if tools can be added to a resource gathering project's information screen. I don't think timber is the only resource that can't be gathered manually but there are very few. If tools were added to the project screen it would have to be worded carefully so that people aren't confused to think they must have a tool for the more than 95% other resources that can be gathered by hand.