MacBook Air M4 motherboard fried shortly after warranty expiration

Before you give up may I suggest another option: take that Mac to a different service center. The reason is that I am not impressed by what iVenus told you, for reasons beyond what they had to say about "constant charge" or "constant load" which as you suspect makes no sense.

A knowledgeable technician, one who respects you as their customer, would not refer to a "logic board" and "motherboard" as though they were two separate components. Choose one or the other, but there is only one such board, and Apple uses the former terminology.

Also, water damage is easily determined. It's not guesswork. Apple calls it "liquid damage" because water is only one such liquid. Other liquids are far worse.

Using jargon like "fried" is imprecise also, unless you were to immerse the logic board in a fryer, and fry it.

All this leads me to question if they know what they're doing.

Not impressed. Get a second opinion.

I would expect any reputable service facility to identify something specific, but that one just provided a number of possible causes. That is not a diagnosis. All they did was confirm something you already knew — broken Mac.

Potential reasons include a defective battery, which can be accomplished for a third of what they told you.

Either they don't know the cause, or they don't care to find out. You should get a definitive answer. If you were in the United States, an Apple Store would provide a definitive answer and propose a guaranteed solution, at no charge.

There are four possible solutions: get it fixed, buy a new one, both, or neither.

The technician gave me a reason that it might be under constant charge.

That does not make any sense. A Mac draws charging power when necessary, so you are correct — those reasons are not logical. Constant load, no load, in between, makes no difference.

Unfortunately these things happen sometimes without explanation.

While it is unlikely that the battery or charging would have caused the problem, it's possible. The failure of the magsafe LED to light may be an indicator there was a problem somewhere in the charging system; or simply that the logic board was in fact bad. There also are any number of other possibilities why the MacBook Air failed.

For the future, this is an example of why I consider it prudent to purchase AppleCare+ with a new Mac, especially a portable model. No one wants to see their computer go bad right after the warranty expires.