This is always a gray area :)
At Gong, most UX copy is owned by the product writing team, except for naming "Tier 1" products. Together with that team, we established a list of criteria that qualifies features or products as "Tier 1;" such as, the feature/product changes core product pillar messaging, or requires customer change management, or changes how we sell or demo the product. These are really dependent on your business.
For in-app cues (like announcement banners/modals, etc), we've established a RASCI model based on the objectives of the copy / in-app cue. I highly recommend starting here.
For example, if the objectives are awareness, monetization, activation, adoption—then PMM is the "Responsible/R," product design "Supports" on visual cues by handing the latest designs to the brand design team to stylize, PM is "Consulted," and product writing is "Informed."
When the objectives are to educate, support the UX, or onboard new users—then product writing is the "R," PMM is the "I."
Even this framework isn't perfect, but aligning on a RASCI for the various types of in-app copy/cues that exist is a very helpful first step.