For FRP pipe, is there a circumstance when the appropriate tee selection type could be, #3 Welding? Is that the typical tee "Type" selection for FRP? Are there other appropriate tee type selections for FRP?

I use #1-Reinforced for fabricated FRP tees and #3-Welding for moulded FRP tees. These terms (farbicated & moulded) are from BS7159.
The flexibility factor is 1. for all tees. BS7159 FRP tee SIF (and the pressure stress multiplier) is a function of the ID and wall thickness of the header pipe.
Fool around with the Tee SIF Scratchpad to see how these data impact your calculations.