Do I need to fix rot when water problem is resolved?

Hello, I have an 1850 house with a situation. I’ve attached a picture of the situation.
Here are the details for the picture. The cause was a leak behind the gutter many years ago. The gutter has been replaced. water leaked down into the wall from the gutter, and now there is rot at the base of the wall on both sides of the interior corner where the gutter joints. The rot extends up about 3-4 feet. I don’t think the rot extends all the way to the outside corner on the right. It extends along the wall to the left about 5 to 6 feet. The rot definitely goes through the cladding and the sheathing in some areas. Not sure about the effect on the studs or the sills. Estimated cost to fix is somewhere between four days and two weeks, and between about five to $15,000. The problem was discovered by the painters who work on my house. They said they would not worry about it for the time being, since the rot has been contained and there is no more water leaking, but they recommended some carpenters, who then came out and did a basic estimate that I shared above. The carpenters wouldn’t recommend whether to do or not to do, but they also seemed to think the rot would not spread further. I’m not sure what to do. Thanks for your help!
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Replies
The microbes that result in rot generally need three things to thrive: a food source, a moisture source, and temperatures between roughly 50°F-80°F. The only one you have control over in this case is moisture. If you are sure that the sheathing not only won't get wet, but not even damp, the rot likely won't spread. There are some microbes that can thrive in more extreme environments so the safest approach is to replace rotted wood. But there is a decent chance you can safely wait a while.
THanks Michael. I appreciate your help.