In general, I sew with good quality polyester thread, e.g., Gutermann, it doesn't create a lot of "dust" from fiber breaking off the thread, and the colors are relatively "duller" (more like natural fibers) than cheaper polyester thread that can be shiney.
If I were a quilter, I'd use cotton thread because of the similar hand (feel, touch) and visual aesthetics of the cotton fabric and cotton thread.
A caution with cotton thread especially, is it can become brittle and break easily with age.
So if the thread in your wardrobe repair kit is cotton, do the strength test suggested by the previous answerer.
For special fabrics, like silk (which can also become brittle and degrade easily with age), I recommend using thread that is most like the fiber content of the fabric you want to repair, in this case, silk thread for sewing on silk fabric.
For delicate fabrics like silk, a strong cotton or polyester thread will be stronger than the silk fabric and can actually pull and tear the fabric (instead of the seam splitting), when the fabric is stretched or twisted in wear.
Since you are repairing silk pajamas that you clearly love and want to preserve, only you can decide if you want to spend the money on silk thread, or a good quality polyester thread.
When you do a lot of sewing, the price of good thread can be a consideration, but if you plan to buy only one small spool of thread, it will a very small extra expense, and you can take the item you want to repair with you when you shop for thread and get the color that goes the best.