I'm interested in understanding how your organizations estimate the complexity of digital initiatives, particularly as a basis for applying appropriate project management governance. In other words, how do you assess initiative complexity in order to determine the level or type of governance needed?

It has been my experience, and is, therefore, my strong view, that there is a strong tension between applying traditional project management governance and methodologies to digital initiatives. The actual nature of digital initiatives just resists estimation heavy and phase-gated approaches.
Digital initiatives, especially those that are aimed at delivering fast, customer-centric experiences and outcomes thrive under agile, product-led methodologies and in fusion teams who manage and govern simultaneously. These are all about continuous discovery, iterative delivery, and real-time course correction. When I say real-time. I mean real-time, not weekly status or planned action. In the morning standup we agree and by afternoon, it is done and we are analysing the impact.
Leading AI models are churning out features almost daily, so anyone incorporating them into digital initiatives, for example, must turn into the complexity. And any digital initiative without AI is.... well not so digital anymore.
In the digital era, complexity is an emergent phenomenon. And so you can't plan it. Any governance model you try and slap onto it is going to result in *overhead without insight* (see Cynefin for more on complexity.)
For this reason, pre-classifying initiatives by complexity in order to then assign a governance model or methodology, through a traditional PMO approach will fail. It's not just me. The leading top 4 consultancies have all described the 70% to 80% failure rate of digital initiatives with a traditional approach. Gartner itself has lots of research about Fusion Teams, Product Management, and Customer-Centricity.
By the way, I put most Agile (2010-2020 style) methodologies with all of their epics and ceremonies into the "traditional methodology" approach. The SCRUM Master often turns into a project manager, trying to project manage the complexity. It doesn't work anymore in this brave new world.
So shift from governance tiers and planning to training people to face and respond to complexity in real-time, within a Fusion Team. When complexity emerges, they handle it. And complexity will definitely emerge in digital initiatives: it is, quite literally their hallmark. And often a source of innovation unless you try and channel the complexity report into a governance tier. Make things smaller, make them faster, train people to just focus ruthlessly on customer impact. 

First of all - the guardrails for stakeholders, project members and project managers need to be documented somewhere. No matter if IT members or not, that helps a lot to get clarity and also rely on something if different perceptions are present. The overall governance I always judge based on: a) how big is the project team b) Who is in with technical skills / IT skills c) How much budget is needed and planned d) How long is the activity/project (3 month / 6 month / more)?

And the most relevant aspect - Can they clearly describe WHAT they want to achieve and HOW they want to achieve that? What is the business value or projected positive outcome?
It is like thinking as you are in the shoes of an investor or entrepreneur.