Although each company has their own way of building and growing their product marketing teams, one way to think about global vs local is based on customer needs and market dynamics.
If the product you sell has the same buyer persona across different regions and the market dynamics are such that the competition is basically the same everywhere, your 'global' PMM team is able to effectively message, position, and market world-wide. If, however, the moment you cross geographic zones the buyer persona or the buying group changes slightly, some competitors become more active in different regions that means you need a more localized approach to how you message and position your product.
I've worked at companies where the product was being sold globally and when I asked customers in Europe or Asia about their needs and whether they wanted product screens in their own languages, they told me that they were so used to English-versions of products for that particular use case that it really didn't matter. And when we looked at who competed with us in different geos, all the same vendors were there.
Another company had a different challenge. We realized that in Europe different personas were showing up in buying decisions. These personas were there because of specific regulatory requirements in Europe that we don't have in the US, and so we started an effort to message these personas and for that we also required some local expertise. This is a typical case where localized PMM is needed.
What is your own situation? Start from the customer and work your way down. Are the customers, the buyers, those involved in the purchase decision the same world-wide? Are the use cases, jobs-to-be-done the same? Are the competitors and market alternatives different? The answer to these questions will help you determine if you need a 'local' PMM team and what differences they would have vs a 'global' team.
This is a great question and I'd say the answer varies based on where your company is in its development. When you've first gone international, you may not have the demand or customer-base yet to validate a full hire per region, so you'll want to hire 1-3 international champions, their job is a mix of market and competitive research, project management, and product marketing. They act as an overlay on your existing product marketing team. Pre-launch developing the research for how your positioning will need to be adapted by region, during launch working with demand marketers to execute on the in-region launch elements and post-launch ensuring that the region is adopting the product and the funnel is growing.
That is really a stop-gap role, overtime that role should evolve into regional specialists within a solutions marketing team that develop full persona-based marketing strategies for their regions.