I am planning to switch to component level stylesheets. Have you done it already? What are your findings? What are the advantages and disadvantages?
In the past
I used to think about CSS stylesheets as stylesheets that might contain the styles for an entire website, including every layout, every 'component', and all of the base styles like what color a link is or the font used for the text.
In the present
For the past ~10 years, responsive web design has become important and the nature of what gets put inside a CSS stylesheet has changed. I think it makes a lot of sense to split apart the structural page layout styles from the styles for the individual components that go into them - especially if the components use element queries for their breakpoints. By having all of one component's styles (including responsive breakpoints) grouped together in a way that can be copy/paste into other websites we can make the parts and pieces of our layout very modular and portable, while keeping our layouts simple to work with as well.
In the future
Imho, both types are useful for different situations. Lately, I am working a lot with Custom Components, and I'd say it's the same for any other component type (Angular, React, etc.). I am in the process of converting them from a centralized CSS style sheet to component-level files, which can pull-in certain global definitions via SCSS mixins. Having the style close to the component code is a boon, because I don't have to search around as much anymore. Also, it opens up whole new features, like only pulling in the component style and wrapping it in a Shadow DOM. Since I use a bundler anyway, there is no real overhead for the build pipeline.
A global stylesheet is very useful for the general site structure, CSS resets and anything which you don't want to put into a component, so I definitely keep that 😉