I am a manager at a FAANG sized company in the Seattle area and had to steer an employee of mine through this when he moved out east at the start of the pandemic. It wasn't a fun thing to break the news to him about this either.
So yes, this is a legal and real thing to have a salary adjustment when an employee changes states or regions. Effectively, he had to sign another offer letter. He was effectively being offered a new job in a new state. There were other incentives to help offset the adjustment.
Something to know. The salary adjustment is not based on the cost of living of your location (as others on this page have erroneously cited). It is actually about getting paid the market rate for tech engineers in your region of the country.
That is, if you live in Nebraska, engineers probably don't make as much there as they would in San Francisco or Seattle. The company doesn't want to pay Seattle salaries if there is limited local competition for business that need your services. It just so happens, that cost-of-living is typically lower in these same regions. But that's not why the company is adjusting the rate. While companies are embracing remote workers, they are also taking advantage of it being less expensive for them.
As such, you likely have some sort of promotion or ladder level assigned to you (based on experience, past performance reviews, promotions, etc...). And the company sets the salary for your role and there's a matrix for what that level pays in each region. It's not your manager's fault, it sounds like they've been diligently giving you raises and promotions during your tenure - hence, they value your work.
So start with this in considering what you are worth:
What do other tech companies in your mid-west city pay for equivalent skills and experience? Do they pay anywhere near the Seattle salary you had before?
And would you be happier working there in your current city for a different company that might be slightly more, but not quite what the Seattle office pays?
Consider the quality of life and cost of living in Seattle compared to your current location. It is indeed expensive to live in Seattle. Housing prices and rent have exploded in the past few years. Food and gas are expensive. And I've known several people who have visited and were aghast at the homeless population downtown. You might find that $150K here doesn't go as far as $115K where you are currently at.
Now, how can you overcome the pain of your salary reduction?
Periodically, in an appropriate way without whining, advocate for promotions and have career discussions with your manager. Advocate for yourself and ask what you need to do to get to the next promotion level sooner. Express to your manager your disappointment with the pay hit you took. You need them to be your biggest advocate.
Periodically scout out new employment in your area. Just having a profile in LinkedIn with the "Open To Finding a New Job" setting enable might get some recruiters contacting you. Do consider that a base salary from a local company might be higher than your current salary, but it probably won't compete with your periodic bonus and stock awards you get now.
Consider moving to Washington State, but not downtown Seattle. You might find that the company's definition of "eligible for Seattle pay" is really anywhere in the state, and not just Puget Sound. (I believe that's the case with my company). Check with your HR department. Then consider if there's anywhere else around here that looks interesting.
You didn't say which company, but we might be co-workers. If you look me up and we work at the same place, feel free to hit me up for more insider tips.