Lacks imagination.
Managing a star is ultimately a matter of being able to introduce material for fusion while removing the products of same. In particular the build up of heavy matter already building up in the core of a star.
This last is absolutely critical because it seems that the formation of iron in a star is its death sentence.
Ordinary matter cannot possibly perform such a function (moving around matter in a star) but it may be possible that plasma constructs can. They would need the ability to maintain their structure and for scifi use I would say the likely route for that is if the constructs introduced stable storms around them, leeching some of the power of the sun’s magnetic system. Then, from that, tendrils of the mechanism would extend downwards.
Each mechanism, in what would amount to controlling the stellar weather, needed would probably be huge (continent sized for any book I was writing ... plus the shielding storms around them) and it would be managed by staff using controlled servo robots, also of plasma, to maintenance and perform all “manual” functions ... their ordinary flesh and blood bodies far from the maelstrom that they are actively managing (Avatar on steroids).
If a civilization can perform such feats they could probably just as easily create new worlds around new stars, maybe even custom made stars.
But if they had built a ring world or Dyson sphere it makes sense to manage their star in this way. With enough stellar gas to harvest or “young” red dwarfs to steal from you could keep such a scheme going for a very long time.
I’ve been saying for months that Tabby’s star, and another one just like it that they’ve recently discovered, may be caused by primordial mini-black holes orbiting within the star itself, around and perhaps even through, the core — but no one is listening... <**sniff**>.
I mean, it’s conceivable to me that primordial black holes, each with the mass of a small moon, say (this would have to be mathematically worked out), and event horizons on the order of a few inches, could plow through the thin material found in the interior of a star as if it wasn’t there, not sucking in much material at all because their event horizons and masses are too small, and yet be able to thoroughly disrupt fusion in the core.