The 2011 cars are in showrooms now, so your car is 13 years old. How are you now, compared to 13 years ago? Like people cars age with the years and miles driven.
Everything you describe is perfectly normal repairs given the age of the Sienna. The life expectancy of the motor and transmission is entirely up to how you have maintained them. Have you had the transmission fluid changed every 30K miles? If yes, the trans might last 20 years. If no, the trans would be ready for boot hill now. Is the motor quiet? Does it use oil, like 2 to 3 quarts needed, between oil changes? Have you had the oil changed every 5K miles? A good motor can last 200 to 300K miles, but things like alternators, power steering pumps and racks, and fuel pumps can fail.
What kind of shape is the body in? How much rust do you see, and how much can be seen if the car is up on the service rack? Rust in Detroit area is a factor as they do salt the roads in the winter. If their is little to no rust the chassis can last another 10 years. But rubber parts like mounts, struts, sway bars, bushings, rubber brake lines, etc. are all subject to failure due to age.
You can keep the Sienna safely and dependably on the road, but your yearly costs for repairs is going to go up. And, the frequency of repairs is going to go up too. There are lots of parts and systems on your car and noone can predict what will fail and when. You can expect more repairs and you need to budget accordingly. $2,000 a year for repairs is a decent figure. Some years will be more than that, and other less, but over the next 5 to 10 years it is a pretty good number. Tires, brake jobs, tune ups, and oil changes are not part of the $2,000; these are maintenance items not repairs.
$2,000 for repairs and another $1,000 for maintenance sound like big bucks. Yet, $3,000 a year is $250 a month. Price out a new, or newer used, car and you'll looking at a much larger monthly payment than $250 and for a lot of months (48) before you own it free and clear.
Quick answer, you should be able to get another 100K miles out of your Sienna if it is good shape now. But you will spend more money on repairs in the next 10 years than you have had to spend to get to this point.