Hi Will... seems you are still waiting on a response on this. I'm no expert, but this is my understanding in case it helps. I hope others can chip and help.
There is no reason that is obvious to me why posterisation would become more apparent recently unless you have changed something, for example, increased application of saturation. It's also not clear why a larger monitor would make it more visible either so I'm not sure that would be a fruitful area to investigate. Understanding what causes it is the best way to design a workflow that avoids it:
In short, sRGB is not capable of displaying all colours on the colour spectrum. It is a relatively 'small' colour space. Have a look at the masp of colours in the charts on this webpage and you'll see what I mean:
https://www.color-management-guide.com/choosing-color-spaces-srgb-adobe-rgb-98-prophoto.html
The colour space is smaller in sRGB than Adobe RGB for example which can be seen by the smaller area on the charts that is covered by sRGB. A simple interpretation of these charts is that sRGB is unable to reproduce the extreme reds and blues and especially the extreme greens as the colour space does not extend out into these areas of the charts. Posterisation will occur when these colours outside the sRGB space are 'mapped' into your file by your image software. In some cases different greens, for example, outside SRGB will map to different greens inside sRGB and so will look different when displayed as sRGB (which virtually all web browsers do by default and why sRGB is usually used for the web). However, sometimes the colours in your image, while quite distinct in the real world will map to very similar colours in sRGB. When this occurs in an area of smooth tone and colour, the small step in colour can be seen. This is posterisation. A smooth gradation in the original full spectrum image reduces to a stepped gradation of a few similar colours that sRGB is capable of displaying.
This can be hard to conceptualise but I hope it helps a bit. Regardless, here are a few things the theoretical observations say will make it worse:
1. Avoid really smooth, gradated backgrounds, especially in the green part of the spectrum. Posterisation is most likely in those. But it also applies to blues and reds to a lesser extent.
2. Adding saturation pushes the colour further outside the sRGB colour space and is likely to worsen posterisation in smooth gradated tones.
3. Try selecting and desaturating an area that is showing posterisation (especially if it is not on your main subject) as that *should* reduce the problem. Not tried myself but theory tells me it should help.
4. Adding blur and denoising backgrounds reduces the variation between adjacent pixels and smooths the tonal gradients in that part of the image and is likely to make posterisation worse. A two-edged sword here as we all like those soft smooth background but they can come at a price. But do avoid adding blur if at all possible.
5. Don't be tempted to save your image into a wider colour space like Adobe RGB. Pretty well all browsers are going to convert it and display it as sRGB - or worse, assume the colour space is sRGB and therefore render them in a way you didn't intend.
Sorry but we are stuck with sRGB and just have to learn to 'live' with it.