First off, this is a "me" problem. I'm not sure that it would translate to others, but I'll try to articulate what it is. Second, "low-budget" is a meaningless term that's probably reflective of my advanced age. I still remember when there were hardly any indie devs, and there was a lot of shovelware out there. Really what it's about is lack of effort, care, or polish in a game, which at this point is largely decoupled from budget, per se.

I think there was a time when turn-based gameplay was popular because it wasn't as hardware-intensive and it was easy to clone turn-based gameplay, at least on a surface level. Between mediocre JRPGs and mediocre turn-based strategy games, turn-based started to look like something that developers were using as a way of saving time or effort, or dealing with hardware limitations. That's not really the case today, as the limitations that existed 20 or 30 years ago aren't there, so it's somewhat irrational. That said, I'm also not nostalgic for that era, even though I know that a lot of people are.

I think my hesitance around turn-based games is similar to how some people in this thread are talking about card-based games. I like card-based games when they're implemented well, but if I'm playing a card-based video game, I don't want it to merely be a digital implementation of an analog card game. There has to be something, like the card game being set in a larger context, or the interactions being complex enough that you couldn't feasibly do it in an analog game. Similar with turn-based games, I don't want to play what is essentially a digital implementation of a board game, nor do I want the game to be banging spreadsheets together a la old JRPGs.

CRPGs with a lot of depth, like Larian's games, are great because every turn-based combat is like a little puzzle with multiple solutions. Something more tactical like Battletech can be really engaging because there are multiple layers to play at, from the mech choices and outfitting to the actual combat. Big strategy/4x games work well as turn-based games because there's an economy and lots of interesting win conditions to explore that require planning and taking your time.

That's more for bigger games, though. Smaller, more focused games can be great with the right execution. I really enjoyed Buckshot Roulette because of how well the developer set the tone. The game itself is relatively straightforward, but the amount of texture and flavor in the presentation really makes it sing. Same with Balatro, a pure turn-based card game, which has so much visual and gameplay polish that you can't help but enjoy the relatively simple mechanics and presentation.

The best turn-based games don't really need to announce themselves as turn-based games, because that's incidental. They're games about something, with turn-based gameplay being simply the design choice that the developer felt was the best fit for the game. I find that when games announce themselves as being turn-based, it obscures why I would be interested in the game, which is why I mentioned it specifically in my original comment. Hope that helps!