If you need advice that particular kind of DIY, feel free to post here and tag me or DM me directly. Hopefully I can be very helpful to some of you folks who either can't afford to pay expensive mechanics or want to learn on your own.
I work as an independent mobile mechanic in middle Tennessee (for now). My primary work is motorcycles and small engines, but I've done plenty of work on cars too. I used to post quite often on r/fixxit back before I left Reddit.
Pic is an example of my work. That's one of my motorcycles, which I resurrected from the dead. I took that picture while was riding to the small town of Cave-In-Rock, Illinois, to rebuild 4 carburetors for a customer, and in line waiting on a ferry to cross the Ohio river.
As to how feasible a suspension adapter plate is: that kind of stuff, and whether certain parts will swap between years, is super model-specific. Unfortunately I can't help you there and my suggestion would be to find Husqvarna enthusiast forums and/or browse through the OEM parts diagrams. My limited experience with non-OEM motorcycle suspension and modifications has told me this: suspension is wildly, massively complicated to design and engineer. You can spend a whole career on it. I looked into revalving a Fox shock for my BMW and ran smack into either buying an $80 software license to run all the figures for me (a complex specific Excel spreadsheet really) or reading textbook-sized papers full of extensive math. So be careful and don't tread new territory unless you absolutely have to, because suspension is very easy to mess up and often hard to get right.
As to sitting for a year: the environment it sat in matters. Was it outside, inside, moist, dry? That will determine how much stuff you need to check over and possibly replace, but no matter what your primary concerns will be two things.
The shelf life of gasoline is 6-8 weeks unstabilized and E10 (standard ethanol-mixed pump gasoline) sucks water straight out of the air. Sometimes you can get away with longer in a fuel injection system that's well-sealed, but never a full year unless the gas got treated with something like Sta-Bil before it sat. You will either need to remove, or dilute, that old gasoline. If the tank was full I'd recommend pulling that gas out and putting it into something else, like a big car or truck fuel tank, where its few gallons can be diluted with a lot more fresh gasoline and it won't hurt. If there's less than a gallon in it you may simply be able to fill it back up to the brim with fresh gas and some octane booster. If your Husky is anything like that one I worked on, the tank won't be a nightmare to remove and that'll make the fuel a lot easier to just turn the tank over and dump it out into a funnel. Your service manual should cover the tank removal procedure in detail. I wouldn't worry about the tidbit of fuel in the lines, but if you're unlucky your injector may be clogged. Try the fresh gas first though. If it won't run with fresh gas then I or a decent Youtube tutorial can walk you through cleaning out a fuel injector (which I actually did on the Husky I worked on, which had sat for 2 years with the same gas in its tank).
Your tires, if the bike has been sitting on them the whole year without being inflated or moved, may have flat spots. You can really only determine this via the eye test, and the ride test if it's not visible. This isn't really a "balance" issue so much as it is the carcass of the tire getting stuck in a bent state. If you can see that one part of the radius of the tire doesn't look perfectly round like the rest, that's a flat spot. Unfortunately the only cure for an obvious flat spot is to replace the tire. If you can't see obvious flat spots, you'll only know when you reinflate the tires and ride. It'll feel like an imbalanced wheel, like you're constantly hitting small bumps in a rhythm that increases the faster you go. Again, only cure is new tires.
Those are the biggest issues.
Any advice on the battery? Should I just replace it with something like a lithium ion battery outright, or can I just stick it on a tender and see if it's still good?
Ah, shoot, forgot about that.
If it's a traditional lead-acid battery and is also the original factory one, just replace it. Lithium batteries are great as they save a bunch of weight, but they're expensive and don't handle the cold as well.
I can't tell you how much I appreciate the guidance and thoughtful responses. I'm not in a position to start getting it going immediately, but will reach out (if you'd like) once I start on her. Thank you again for your time and knowledge-base.