There is a link in my signature called "softened water" and it goes to a thread that I had posted in 2018 of my water softener installation. Like you, I also had the standard 1-1/4" softener loop inside my garage. Luckily, dumb luck really, that my auto fill line was run from a spigot off my garage and along the side of my house to the pool. Therefore, all the plumber had to do was run an additional 3/4" copper line out through my garage wall (easy point of penetration with little or no stucco damage) and then we dug down and transitioned it to PVC and the autofill line. It was a lot of dirt work to dig up the line but, all in, it only added an additional $600 to my softener install. Well worth the price!
If you do something like that, make sure there are plenty of 1/4 turn shutoff valves installed so that you can pick and choose what you want to shutoff. The way my softener is configured, I can do a "vacation" shutoff where all the softened water to the house plumbing is shut off but I can keep the pool autofill open so that the pool has fill water. I also have a shutoff valve outside so I can kill water to the pool in case of a catastrophic leak without having to run into the garage. Lots of ways to to do this stuff just engage the plumber before you kick off the job and you can easily figure out what needs to get done.