I would imagine it is fairly carbon neutral... you are burning things that grew over the last year. You aren't releasing new carbon into the air.

This isn't quite right. Technically it's carbon neutral, but the alternative method is carbon negative, as a larger portion of decaying matter will sequester carbon into the soil than would if you didn't burn. So the reality is that this is not carbon neutral compared to the alternative.

Of course, there could be some hidden factor I'm missing, as biological systems are complex.

biochar is actually considered a carbon sink, because the carbon is not readily released, unlike organic carbon.

So burning forests or seasonal burning like in Indonesia is carbon neutral from that perspective?

Seasonal burning probably is carbon neutral.

Burning forests, not so much (at least by standard definitions of carbon neutral). 'Carbon neutral' requires a reference frame; we usually mean from the perspective of the people doing the carbon releasing. If you burn a forest that you planted, you are carbon neutral. If you burn a forest that has been there for centuries, you are not carbon neutral.

My mother has several blueberry bushes in pots, she mixes coffee grounds in the soil to get the acidity needed to have them grow again. However, I'll propose burning, just to see the reaction on her face.

Can't edit, but I informed her and there is a potted bush that is underperforming this year and so she's open to trying the burn method to see if it helps.

the more modern and hip way is to use not-a-flamethrower