How technical should one be if they are interested in being a Developer Product Manager?

As a Product Manager, you need deep knowledge of the personas you serve. To build great products for developers, you don't need to be a developer, but you need to understand their challenges, motivations, and day-to-day work. I encourage product managers to use the products they build so that they truly understand their users' experience. This means that product managers for developer products need to be more familiar with software than product managers for other types of products.

Quite technical, because you cannot have the requisite level of empathy for the target user, not to mention be credible with your engineering team if you aren't. Now, I do think that a mistake that PM hiring managers for devtools often make is trying to optimize for specific knowledge in a particular domain (e.g. if you're an observability company, trying to only find PMs that already know monitoring/observability). This is unnecessary. What I look for are transferable technical skills: have they been a software engineer/devops/SRE before? Or worked as a field engineer (sales, post-sales) for similar products? Knowledge of the domain can be acquired over time, but the candidate definitely has to have a basic aptitude for technical problem solving and not be scared of getting their hands dirty in touching the product.

One way to evaluate this is to have them demo a technical product that they have familiarity with or worked on in the past.

I assume by "Developer Product Manager" you mean a Product Manager who is focused on developer-facing Products, like APIs or infrastructure tools. I've worked in the API space for many years, and have trained people from a variety of backgrounds to become PMs in the API space.

I find that these roles should require more technical knowledge than the average PM. In general, PMs need to have some skill in design, some skill in business, and some technical skills, in order to be effective (design a usable product, align plans to business needs and work with Sales/Marketing/etc to launch, and work with Engineering to build your products). It's beneficial to also stand out in one of those 3 areas, like being great at design to work on customer-facing interfaces, or on technical to handle developer-facing products or integrations.

For a developer-facing product, I require more technical skills simply due to the importance of customer empathy. If your customer is a developer, to have strong empathy, you have to understand the real challenges they face as developers.

I myself have a Computer Science degree, and while I've been in Product for 16+ years, I still write code to maintain developer-empathy. I continue to write code even after having become a people manager a while ago.

That said, many of those I trained to become successful "Developer Product Managers" didn't have technical backgrounds. I often hired them into other roles where they could interact with our developer community, while teaching general Product Management principles, and encouraging/obtaining a subsidy for coursework in programming. A good programming course (no need for a degree or even a bootcamp), combined with on-the-job experience in Developer Support or Developer Relations to interact directly with developers, can provide enough experience and technical chops to do the job well.