Is this the sort of situation where you could drain a greater part of the pond and have it fill up again readily?

As for trying to muck it out with a bucket, keep in mind that the rule of thumb for one thousand square feet of area is one inch of depth is three cubic yards of muck. That quickly adds up to a lot of moving for small gains if one is doing it by hand under water.

People can do this type of thing as long as they're willing and stay at it long enough. I don't know how large a spot you want to clear.

Best way to tell is give it a try. You'll know very quickly whether the job is for you or not.

A lot depends on the pond. If it has a solid bank its a lot easier than if you sink in 1/2 way up your leg.

In general this type of thing is not super effective. Depends on the pond. If you're able to pull out some cattails it's pretty likely some bits of root (rhizome) will be broken off and sprout again pretty fast. If you only clear a small space the surrounding plants will fill in pretty fast. Removing string algae will often grow back.

It's more like mowing the lawn, it comes back.

Chemical can be used on cattails.

If the work gets to be too much you can try a pond/lake weed cutter. They make different kinds including manual. It doesn't kill most plants, but if you stay with it and cut back when the leaves break the surface the plants can overtime slowly die back. I think that's less work and more effective than hand pulling which kind be hard/impossible.

Thanks to folks commenting so far.

Well, the area I want to clear up isn't too large, just a few feet wide going a few feet out. Perhaps about four feet to six feet wide going out three to four feet at max. So more like a couple dozen square feet rather than thousands, though the math is good to know.
And I just want to clean it out enough to drop in a tiny floating dock again.
The algae isn't too bad really, I think it's because the area is so overshadowed by the willow. Looks like most of the gunk is plant debris.

Don't want to use chemicals- we have flourishing wildlife I don't want to risk with chemicals and I don't want to kill all the cattails, just clear out a thin spot of them.

I think the original owners had this spot cleaned open a lot more than I'm planning on. You can tell it was cleaned out nicely at one time. And it really hasn't grown in much in the three years I've been living here. But I want to start tending this spot now before it gets any more grown in. Start maintaining it before dropping in the little dock.

The little dock I'm planning on will be one barrel wide, about 3 feet. Probably using 12' long boards. Just enough to stick out into the water a little bit for one person to walk out onto. No boat launching or anything like that. More of a wildlife watching spot.