As far as I know the solution used for sinus rinses is isotonic to the cells. Although I'm not sure if those microbes need the same salt content as humans (0.9%), but I would presume so.

If you double the isotonic solutions, don’t they become hypertonic? The instructions that came with my Nasopure say to use two packets for a hypertonic solution.

You can also make your own Nasopure by mixing 9 g NaCl and 6 g NaHCO₃ into 1 l of water.

No. If you have a 1% solution (to pick a number) and you add more 1% solution, it doesn’t become 2%.

If you add two packets of salt to a fixed measure of water, the solution is (roughly) twice as salty as adding a single packet.

The particular microbe here has a cyst form for inhospitable environments.