Sludge in the oil of a Subaru Forester

My Subaru Forester has 105k. For the past three years, I've had to add oil to it at an increasing rate. In the past few months, I've had to add a quart every week or two. I have recently found out that this may be a common problem and that Subaru extended a limited warranty to cover it. Impressively, Subaru has agreed to address the problem for me, even though my car has crossed the 100k mark. (They are compensating me for a rental while my car is in the shop and offered to pay the towing fee which turned out to not be necessary. So I'm very impressed with the attitude from Subaru.)

I just received the following pictures from the Subaru mechanic. I've asked for a clarification, but posting here while I'm waiting for a response. There's sludge in the oil and the radiator.

Pictures

Given my car's history of burning oil, I can't help but think that the oil consumption problem and the fact that I've had to add oil for a few years, is related to what the pictures are showing. But I'm not an expert in any way, so hoping for some expert opinions here.

Edit:

The mechanic did not offer an opinion on what may have caused this, but shared the following:

LEFT SIDE VVT TIMING OFF. MULTIPLE MISFIRE CODES. CODE FOR CRANK AND CAM TIMING A FAILURE

NEED TO REMOVE TIMING COVER TO ADDRESS CONCERN. FOUND COOLANT IN ATF COOLER LINES. FOUND RADIATOR CAP EXPANDED. TECH WOULD NEED TO START BY REPLACING CAM SPROCKETS. REPLACING TIMING CHAIN, AND REPLACING TENSIONERS. DURING REPAIRS THE TECH WOULD ADDRESS THE ISSUE WITH THE COOLANT/RADIATOR AND REPLACE THE COOLER LINES AND RADIATOR.

TO START PARTS ADD UP TO $1785.79 LABOR IS APPRX. $1,950 DIAGNOSIS $115 TOTAL $3,850.79