I have an opportunity at work to cut back to 32 hours a week instead of 40. My benefits won't be affected, but my salary would drop 20%.
Do it. I've been doing 32h weeks for nearly six years now, and I cannot speak highly enough of it. Three day weekends every week, plus extra long weekends often enough, and the ability to do far more around the house and property than I would otherwise. I live rural on what was a bare lot, so there's no shortage of things to work on, maintain, improve, etc. Current project is a 600 sq ft Trex deck, then maybe some stairs on the other side of the house to replace the increasingly inaccurately named "temporary" stairs. The local school district is also only on 4 day weeks, so Fridays match their time off, which means we can do stuff on a family for the long weekends easily, or just head somewhere fun on a Friday and skip the weekend rush.
Your salary drops 20%. This trims off the highest tax bracket. Your benefits remain the same. And you have a 50% improvement in weekly days off. It's worth it. Do it.
It seems awfully extravagant to "pay" for so much free time.
Sorry to be trite, but do you live to work, or work to live? Have you structured your life around all the expensive luxury goods, or around something different? If you'd do exactly what you do for work in your free time, and the money goes into the "must have" luxuries you read about in various "Things you can spend money on!" magazines, well... I don't know what to tell you. Keep working, earn that money, vacation... wherever that happens to be.
We've structured our life as a family around less of that, and so the lack of extra income doesn't make a big difference. We spend substantially less than comes in on regular spending, and the surplus time and money goes to things like decks, camping, a side business I'm funding R&D on right now, being able to be generous with our time and money, etc.
Not sure what I'd do with the extra time. A more interesting part-time gig/job, write a book, code a video game, volunteering, new hobby? Do I need to commit to a plan before I pull the trigger on more leisure time?
Sleep in, wake up, make coffee, sit outside with a good book and drink the coffee, go inside, make some bread, toss it in the oven, clean the kitchen... go build something with random scrap lumber.
If your job doesn't drive you nuts and covers your expenses, go find something interesting and enjoyable. Reject the whole "hustle culture" thing in which you have 10 "things you're working on" at any given point. If you've got the cash for your desired lifestyle (which can be adjusted on either side - our truck is old enough to drink and the car's almost a teenager), don't worry about trying to turn the extra time into money. Enjoy it. If you find something you're good at that's profitable, so be it, but don't force it.
Also concerned that while I'll have permission to off one day a week, my overall responsibilities may not decrease much. I'd hate to take a big pay cut if it comes with the expectation that I'll be just as productive in four days as I am now in five. My boss is aware that could be an issue, and thinks he can temper his expectations. I'm not convinced.
Depending on what your work is, "Time in seat" may or may not correlate to productivity. I've occasionally tried to force solving hard problems with extra butt-in-seat time, and it rarely works. Take the weekend off, split some wood, beat on rocks, build a deck, change oil in stuff... and I'm reset and often able to solve things on Monday that were driving me nuts on Thursday.
Try it. Worst case, you can just go back to 40h, right?