My cat roams the house meowing loudly and tragically, but only at night, starting around 11.30-12 and going until ca 3-3.30. If, on occasion, I give in and go to check that she's all right, she'll stop for the duration of our interaction but start up again once I leave the room. It's fairly clear what the issue is: she goes outside whenever she likes during the day, but I do keep her in at night - so she'll sleep in her favourite chair until ca 10 pm, and then not have got enough outdoor time/exercise before I lock her in for the night (11.30-12, coincidentally). (Would leave her out but there's a fox and a few big male 'did you spill my pint' neighbour cats, and no cat flap as she kept bringing in mice.)
Jackson Galaxy, the American cat expert who is actually rather lovely, believes the only way to deal with constant meowing is to completely ignore it and act like it isn't happening - don't interact at all in response to the noise so it doesn't bring the cat any benefit. (Apparently adult cats don't meow to each other, only to humans, and it's a help-requesting behaviour, like kittens mewing to their mum.) So far this strategy has affected my cat's behaviour not at all, but hey, it's only been several years. I've also tried environmental 'enrichment' so have set up what I call the kitty gym, an elaborate construction made of Amazon boxes woven between the furniture to make an obstacle course of sorts and garnished with strategically-placed toys, and actually that's helped somewhat - I bring it out at bedtime, have a short play with her in it, and then leave it set up in the room furthest from the bedrooms. She does hang out in it, which means the meowing is at least sometimes far enough away for the humans to get some sleep. According to Jackson Galaxy's copious video output the answer to almost every cat problem is more enrichment in their environment - and your cat may be a good candidate for this, as you say she shuts up when you give her attention but is otherwise meowing? Jackson (we're on a first-name basis given that I've watched approximately 7,000 of his videos) recommends additional 'cat tv' window perches, more things to climb and scratch, and in general what he calls 'catification' of your house. YMMV, but he seems to have had great success...