Here's my experience with wood ash on my garden.
We burn a lot of wood, so we get buckets of ash over the winter. Almost all of it is from oak or maple; sassafras or elm occasionally, pine for kindling, so not often.
One year, I went out with a bucket and used a cottage cheese container as a scoop. I sprinkled it around until the bucket was almost empty, or so I thought. I tipped the bucket and dumped it over about 20' of area. Well, there was a lot more ash than I thought, and it ended up pretty thick.
I did this in the middle of winter and planted alfalfa in that area in the spring. You could see exactly where I had dumped too much ash. And where I emptied the bucket, the alfalfa barely grew.
I haven't put ash on the garden since then. I dump it out in the woods or the field. I thought with all the oak leaves I use that the soil would be very acidic. Nope. Not sure why, but it isn't.
When I mix my own potting soil, I use about 1 cottage cheese container worth of ash to add some minerals.