By no means my area of expertise, but a quick glance suggests:

The experimenters set up a system that could detect slow-wave (SW) fluctuations in brain activity. They used trans-cranial magnetic stimulation (electro-magnets on the scalp) to "augment" this SW activity. This seems to have improved memory, measured by some specific learning task they set for the participants.

Trans-cranial magnetic stimulation is becoming popular in trans-human type circles. Apparently it's becoming feasible to do at home with cheap off the shelf components. However, of course, the long term effects and side effects are poorly understood.

This particular experiment used 16 participants (only three of whom were female, for some daft reason) so we can't draw any firm conclusions from this.

Not magnetic, electric it looks like. I’m not sure how I feel about running electrical current through my brain.

Apologies, you're quite right, they're using "transcranial alternating current stimulation" a.k.a. tACS during sleep. Now I'm at my desktop I can read the paper, and see that they applied direct current during task training (discovery of "hidden targets in static images") using the "StarStim R32 simultaneous EEG/Stimulation device", and their own tACS system during sleep.

ECT(Electroconvulsive therapy) is already a thing - it is used for various treatments for depression and seizures. It consists of small electric currents passing through the brain which is very similar to brain stimulation, the only difference is that he first one is a medical procedure while the latter is, as of now, more like a brain hack. I wouldn't recommend anyone doing it without knowing the risks involved.

I don't think it's accurate to describe ECT as using small electric currents. The very name says that the procedure induces convulsions.

From Wikipedia: "ECT is often used with informed consent as a last line of intervention for major depressive disorder, mania, and catatonia. ECT machines have been placed in the Class II category (special controls) by the United States Food and Drug Administration (FDA) since 1976." (Emphasis mine.)

It sounds like hard rebooting a mind.

I feel like it sounds like a really bad idea.

The use a brain "massage" device on a person while they sleep and they see their longterm memory improving. Brain improvements are a big business and a lot of people have got ill for trying these stuff at home. https://www.bbc.com/news/health-27343047

Doing this stuff on yourself at home is pretty much an equivalent of trying to tune up your car's engine by randomly smacking it with a hammer while being blindfolded. You probably will not break it completely, but it's also very unlikely that it's possible to improve something without understanding how it works first...

Putting aside the fact that a lot of progress in history (herbs and medicines) have been found exactly this way, through trial and error and some 'mystic' guess work.

I don't think we are close to understanding the brain either.

And a lot more and focused progress have been made by people that study the subjects extensively, and try "things" and scientifically measure the impact.

from another website.. "tACS: Transcranial Alternating Current Stimulation (tACS) is a noninvasive, low-level alternating current applied to the cranium. New research out today suggests it expedites memory consolidation while you sleep. As with the above noninvasive transcranial stimulation techniques, it is not fully understood how it works and the long-term effects are unknown." - https://www.forbes.com/sites/andreamorris/2018/07/23/can-we-...