Atcone, in spring summer and fall, I use softened water from an especially plumbed outdoor soft water spigot for my pool and hot tub.
My hot tub repair guy, who replaced my 15+ yr old jacuzzi dual pump two years ago, is against this move, and claims its corrosive. However, note said pump was more to 15+ years old (actually closer to 20, I think) AND that in terms of salinity my hot tub water is lower than those that use SWG for their hot tubs. So my OWN take is that the soft water is fine, but do change it periodically so it doesn't build too much salt.
In the winter, my shop water source closest to hot tub is raw wellwater with high-ish iron.
Originally, I used this to contol metal, one dose on start up:
Amazon.com : Leisure Time D Spa Metal Gon, Pint : Spa Metal Gone : Patio, Lawn Garden
(Note this is not a brand we recommend for pools...but is suited to hot tub size.) But in my case, in snowy cold ams I'd periodically forget to use the weekly "defender" and I'd get yellow-orange tint back.
I've since experimented with a spa/pool pre filter with an alleged 8,000 gallon capacity. If you read the Amazon reviews, it gets four stars but some say it doesn't work. Others say is gets much less capacity, eg 5,000 gal before loosing effectiveness. Also note that neither. Pre-filter OR water softening system actually COMPLETELY removes iron once its in the 2 ppm range...above 2 ppm, "iron curtain" type maganese fiters are allegedly more effective (and expensive

Read...and possibly use this far less expensive option...at your own risk
Amazon.com : Pre Fresh Garden Hose End Water Filter all purpose, pool, spa, hot tub, pets, car wash : Garden Hose Parts : Patio, Lawn Garden
In my setting/condition/level of well iron (aporox 2 pm raw) his particular prefilter works for me and prevents both tinted water and stains -- without it, orange tint upon shocking. However, I suspect efficacy and the mixed results reported with pre filters kinda depends on HOW MUCH iron you have in the water, how much builds up in the water etc. So YMMV.
Those of us with wells have to experiment a bit to find the right balance for our unique parameters. My preference is soft water, then adding calcium to 150. But in hard winter, I can't make that work or I blow the back flow...
(ask me how I know
Best wishes for swift do-over and some nice autumnal soaks
