Really depends on if there’s a significant drop or a very high spot that you want to set as the leveling point for the floor.

The overall floor is pretty level, just the glue and some splats of drywall mud

I would get a flooring scraper and get most of the glue off before doing anything, self leveling or other

Glue will have to be removed before you do anything

Yes, it will give a much better finished products. Use the self leveler and then sand before flooring installation.

When I try scraping though it digs into the wood. I'm worried I'm doing more harm than good

Yes. If you skip it and you do not have an excellent surface below you will absolutely regret that decision.

I recently put down vinyl tile down on a cement floor using tile adhesive underneath. This was for a school we were renovating. A huge room. The old floor had tons of dip and bumps. After I was done, using a rubber mallet the whole way through, it looked awesome. Bumps and dips basically disappeared. I didn’t use a self leveler.

A contractor friend of ours who had seen it before couldn’t believe how good it looked and wondered how I did it, especially since this was the first time I done anything even remotely like this.

I think the adhesive really helped leveling it somewhat. I didn’t lay it on thick at all but it came out great.

So you may not need to use a self lever to get a good result.

Get a belt sander with 40-60 grit. Be prepared to go through tons of belts as the glue will foul them quickly

If it's not level you wind up sticking things together at angles that are slightly different from 90 degrees. In a small space it's not a big deal. In a large space you wind up with gaps and overlaps as you move across the room.

That will need cleaned up, use a sander if needed.

Get/rent a floor or belt sander

You can lay vinyl on a concrete floor as long as it's relatively flat - it can slope up and down like basement floors tend to do (the vinyl can take slopes no problem) but OPs picture is rough and jagged; I wouldn't do that.

It's the much easier solution than trying to clean that stuff off

Wouldnt the heat of the belt sander gum up the glue?

Boiling water and a towel. Work fast, little areas at a time so as not to damage the floor. Just dump the water, cover with towel, couple minutes later scrape and dry.

This sounds like a terrible idea. That will mess up the wood floor for sure. If you want heat, use a heat gun and a scraper, not boiling water.

If you dry it quick enough, it's fine. Don't use a lot of water, obviously. The towel will soak most of it up before it can really penetrate the wood.

Vinyl will telegraph whatever is below it. Even a small pebble.

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That glue is probably so old and brittle that it wouldn't.