At what stage should product marketing collaborate with product design on the design process?

Design and Marketing should ideally go hand-in-hand. 

If the Design team is very mature, experts in the area, and functioning on a world-class level, then Product Marketing's input/review can be focused on later stage designs, possibly as key stakeholder sign-off.

In younger organizations where Design is still a developing area, Product Marketing can and should add value to every stage of Design. In my experience, it can be helpful to frame input in terms of PMM competencies (e.g., research, interviews, surveys, competitive analysis, market data) to avoid being perceived as over-steppping bounds.

If I understand your question correctly, constantly. No matter if you're the lead product marketer for an enterprise product, SMB, or consumer; whether you have a product-led go-to-market or a traditional enterprise sale; product marketing and design are inextricable partners in a product's success.

Just like pricing is marketing, product design is also marketing. It's how you (your product) explain your value, function, and potential use cases to the end user. If you need to show how your product can be more efficient than a competitor, work out a better flow with UX. If you need to understand exactly why a competitor is perceived as more usable or scalable, ask UX to break the task flows down for you. 

Practically, you want your website to reflect the absolute best of your product in action. If your product team and your brand/web/design team aren't in sync, you're going to be setting the wrong expectations. 

Beyond that, at least half of a product design's team purpose is to deeply understand your end users. Their challenges, priorities, mental models, hopes, and dreams. That's persona gold, whether your end user is a buyer, an influencer, or both. And it's a win-win relationship; you can learn more about your end user in 30 minutes than a month of research, and your design team gets equal insights into the buying process, where friction exists, what other use cases exist in the market that might be competing for attention, or adding friction to the process. 

At the stage before anything is handed over to eng for design. At Atlassian, we refer to this as the "Explore" phase–"Wonder" and "Make" come before and after, respectively. 

When you do this, be clear on the role PMM is playing and the type of feedback the design wants and needs to move forward. In my opinion, that feedback should not be focused on visual design.

In my experience, it's best if product marketing is in lockstep with the product triad (product manager, designer, and tech lead). They should all have a really clear idea of what they're building and who it's for. There are two parts of the design process where PMM might be a bit more involved:

UX Research

As a product marketer, I've found it valuable to sit in on UX research calls to hear firsthand how customers are interacting with the product. This research can help shape final design decisions and provide insights into how users are describing the product in their own words. If the company doesn't have a research function or work with an external research agency, then product marketing may be more involved in this step. Otherwise, product marketing is really just listening in and staying informed.

Content Design

Ideally, there is a content designer on the team who can think holistically about how copy shows up in the product and its role in the overall user experience. However, in cases where there is no dedicated content design team, product marketing can be helpful in reviewing in-app copy. This collaboration typically happens towards the end of the process, after the UX designer has prepared near-final mockups.

Overall, I think it's best when you're able to tap into the specialized skills of a UX Researcher and Content Designer. If your team is much leaner, product marketing will likely need to step in and help provide additional support where there are gaps.

My experience has been that product managers work with product design directly. I personally have not engaged with the design process beyond seeing their concept videos or Figmas. We communicate our design expectations or product experience needs to the PMs directly.