How to recreate drawstring effect on this dress on homemade nightie pattern
There are a few things to be considered here:

Comfort

Are you sure the drawstrings will be comfortable when lying down, either on your back or your side? If you aren't sure, consider pleating instead.

Will you be able to ignore the loose ends of the strings or will they bother you? You can keep them shorter than shown in the picture (sew them in place) or pleat the fabric instead.

Pattern

The front is basically a big rectangle with a very narrow triangular neck that gets stretched by the drawstrings. The width of the front panel looks a little wider than the width of a well-fitting t-shirt. I'm sure you can adapt a simple tunic pattern.

Unless you want a drawstring at the back as well (keep your comfort in mind!), the back must be cut to your actual size. That poses the problem that the shoulder of the front panel is wider than the back. You either have to cut the back panel wider from the waist up, or find another way to fit both pieces together.

Construction of a drawstring

I assume the fabric for your nighty is rather thin. In that case you should encase the drawstring on all sides to protect the frabric from wear. Cut long rectangles (the width depends on the size of your strings), hem the short sides and sew the long sides together to make tubes. Iron the seams open right in the middle of the tube (will be the underside). Place the tubes on your nighty seam facing down and sew then in place along the top and bottom edge, then insert the strings.

If that adds too much bulk, you can get away with encasing only the top of the drawstring. Cut long rectangles, hem the short sides and sew them in place with the cut edge double folded inwards.

Tips

If you have any cheap fabric like muslin lying around or an old bedsheet you want to throw away, make a mockup before cutting your desired fabric. This helps you finding the correct size and refining your pattern.

If you don't want to make a mockup, I advise drawing the pattern without seam allowences and then adding generous seam allowances all around (at least 1.5 inch / 4 cm, more is better). This gives you enough fabric to gradually refine your pattern.

Remember: you can always cut away, but you cannot uncut.