Have you tested your hard water? Mine (in Katy) is 100 to 125 CH the 3 or 4 times I tested over the past couple of years. I have my fill via the softener and have added some hardness increaser occasionally. However, I have also hooked up my hose and added the hard water on occasion. So it really may not matter which way you do your hook up if your CH test is about the same value as mine. I run my CH at 250 to 325 with no issues. The only thing you need to be aware is that the only way to reduce CH is by draining and refilling so you do not want to get in a position of dealing with high CH on a continuous basis.
I haven’t personally tested. Might ask my neighbor that has a pool to see if he can test for me.
I’m in sugar land area in MUD128 but can’t find any data on my specific one for some reason.
But all the other ones around us and main sugar land look to be in the 130 range. If it’s in fact around that based on what your saying it won’t really matter?