It is based on operating temperature. Let it slide. Keeps the structural/foundation engineers happy and it won't damage the vessel or its supports. Light ones just need steel to steel slide plates, but heavy ones need plates with teflon backing.
“What I told you was true ... from a certain point of view.” - Obi-Wan Kenobi, "Return of the Jedi"
It depends on the layout of the piping. Generally, the end near to a pipe rack would be the fixed end, but there are additional considerations. Think about how you would bring the piping up the vessel, and where you would anchor/guide the pipe, and that will inform your decision on the fixed/sliding end of the vessel.
Be sure you put the slide plate on the saddle that has the slots in its base plate and if the fixed saddle isn't on the piperack side, inform your supervisor. Why are your saddles marked "typical"? Sliding saddle needs slots for the anchor bolts. Round holes needed for the fixed end. The notes should reflect which is which.
“What I told you was true ... from a certain point of view.” - Obi-Wan Kenobi, "Return of the Jedi"
IT seems we are dealing with a sulphur unit reator. High temperatures are involved, around 400ºC. Normally the outlet temperature side of your reactor, where the temperature is higher, is where designers put the sliding point sadlle.
Try thinking it through... If you have anchors in the piping near the heat exchanger, that limits (or theoretically eliminates) the piping's ability to move at that location. Therefore you want the equipment support near the piping connection to be fixed so you're not creating additional forces on the piping. You should still analyze the piping and confirm the arrangement is adequate.
If this is a high temperature application, the piping and equipment want to grow (expand). If you're equipment pipe nozzles are also growing into the piping anchor, you're compressing a pipe that wants to expand. There'll be gigantic forces and things will break.