Dunno if they've been brought up already, but I like some of the minigames in Being a DIK. English takes me back to my youth playing Bully, the new Chemistry game was pretty simple yet engaging, and most of the little games through the phone are enjoyable too. The fighting(Brawler) and the color tic-tac-toe one(Triple Tile).
I guess I'm in the minority because I kind of like minigames. It might be my ADHD but I appreciate when a game breaks up big blocks of text and images with something new. It gives my brain something else to focus on. My only real problems with them are if they are poorly programmed (too fast, too buggy, etc) or if they are overused.
I know that feel. Imagine reading relaxed through some ok story between good sex scenes and suddenly being interrupted by some reaction based or time limited mini game. Just awful. I don't like it.
I feel that as long as they are well thought out and implemented, then I'm cool with them being added as it help me to switch my brain back on after reading a lot of text. but I think the best thing to do is to just allow people to skip if they want ( I disprove of games that penalize people who do skip however.)
Obvious answer for me is that it depends on the mini game in question. But as long as they are optional, which it is in many of the games Iäve played. I am all for it. Sometime it can be quite fun, but if I want to jump ahead, I should be give the option to do so. I don't play the games for the mini games, if you catch my drift
If so, I am generally in favor. Examples of minigames that fit the narrative in visual novels:
representing a fight by making the player decide whether/how/where to dodge or attack in each round, based on some visual input of what the opponent is doing
battles like in classical RPGs
single choice, mutiple choice or even free text questions representing school tests/exams taken by the MC
having to click something on the screen quickly in situations in which the MC must react quickly.
Even AAA games use minigames, and not always in a good way. E.g. I absolutely hate the lockpicking minigame in Hogwarts Legacy. It fits the narrative, but it isn't a good game at all and there are silly restrictions on skipping it.