What is going on here with these mushrooms?

Everybody here is working at fostering fungi growth, but I'm seeming to be going into another direction and I'm not sure what to do with it.
I've recently begun  working another urban garden project, but for the first time in a temperate zone.  I'm originally from the Big Island of Hawai`i (Ahhh! Miss that perpetual springtime!) and we don't have winter kill there.  We can even make annuals into perennials!
A little history first:  Spring of 2020 - Rototilled every square inch of lawn we could find, buried it all under 8 inches of wood chips (free from the city wood lot), Planted my soil block veggies on a square-foot plan.  I had to get some food planted while figuring out what to do. Got a great garden.
Last year was the first season in this climate, then came October!  Arghhh! Everything died!  So disappointing and so cold!  I couldn't even go outside until the temperature reached an unfrosted, non-numbing temperature of 60 degrees!  (Average year-round temp in Kialua-Kona is 72 degrees).
So, being the persistent permie we all are, I started again this spring and after winter mulching with spoiled straw, my soil was looking beautiful though alkaline.  The standard answer was more compost and things began to look a little livelier.
However, while my soil blocks were sprouting, I had to go to Spokane to wish my Mom a joyful transition as she passed away.  And when I returned, I found this: mushrooms covering the woodchips. (see pic attached).  We don't get this in Hawai`i,  We mulch with lava chips (kidding). We're mostly chop and drop folks. We be da lazy, bruh!

So, what are these?  Are they edible? Do I leave them, gather them for compost, or what?  Totally out of my league here. I wanna go home to eternal spring where no fas' fast like here!

To properly identify mushrooms, we would need an approximate location and close up pics of the top of the cap, the underside and the stem.  You can do a spore print also.  I do not recognize them but I am close to the Gulf of Mexico so not everything grows here.  There are some excellent mushroom id groups on FB.

Since my last picture, I gathered one large green waste container and 3 large construction garbage bags full of mushrooms.  I've got stashed along the pumpkin/melon/cantaloupe patch until I know what I can do with them.  I'd hate to dispose of them off property if there's some usefulness to them.

Here's a couple closeup pictures from the newest batch that showed up after a 3 day rainy period.

I'd appreciate anyone giving me any information on them.  I was unable to fine any info.  Everything I found was about edible mushrooms and foraging.  No need here, the bloody things are everywhere I put don wood chips!

Those mushrooms look a lot like Agrocybe praecox, an extremely common woodchip inhabitant. See if this looks like a match:

http://www.mushroomexpert.com/agrocybe_praecox.html

I see these all the time, they're one of the most common wood chip mushroom. They are not edible and smell awful, at least to me. But they help make great soil.

Thank you!  This info was spot on regarding the description of my mushrooms.

So, I should be able to compost these in my compost pile and be able to spread them under heavy mulch next fall to winter over for 2022.

Am I correct in that assumption?  I really hate let so much organic matter get away from me!

Yes! Absolutely great to compost, but you really don't need to remove them from your beds- they won't compete with your veggies and may well benefit them. some cool mushroom growers ( I remember seeing a video in another, thread, I think?) try to create ways for edible mushrooms to thrive in beds, but even inedible mushrooms add to the ecological diversity and fertility of your beds. I actively encourage mushrooms in my beds/food forest, and sometimes I get lucky!

They weren’t in my beds but in the walkways I currently have. So, my plan is to to compost then and use them in the sheet mulch at the end of the growing season. I’ll thick layer mulch and amend to bring down the pH to a reasonable level for next spring. Thanks for the help, I really didn’t want to throw all that organic material away.