A 36 door has a rough opening width of 38 so your header is cut at 41.
Header above sliding glass door.
The existing header is 2 2x8 and is actually long enough for the new door.
So for piece of mind i am leaning toward replacing the header to avoid future problems.
We are installing a new 6 sliding glass door to replace an existing window.
Also be aware double or triple jack studs may be required based on the opening width and the load the header carries.
Doors in a load bearing wall that holds the weight of the house created by beams and trusses need a larger header than those in non load bearing walls.
A typical header width with single jack studs is cut 3 larger than the rough opening.
The header is usually made out of dimensional lumber installed on its edge.
The longer the distance a header spans and the heavier the load it supports the more substantial it needs to be.
However all the header sizing tables i have seen require 2 2x10 for this size opening.
Calculating window and door header requirements is complicated because they depend on a variety of factors including the size of the opening the weight of everything above it snow loads if it s an interior or exterior wall and more.
For header spans see tables r502 5 1 and r502 5 2.
Together the headers king studs and trimmers act as a system that transfers weight from above down and around the window and door openings to the floor and foundation below.
If you have a floor above you ll need 2 2x6 s unless the building is 36 wide in which case you ll need 2 2x8 s.