We do. Our [internal] wiki article on technical debt explicitly covers examples, guidance on when to intentionally take on debt, how to document and measure it, different "grades" of it, and how to plan to retire it.
There are then per-application technical debt pages for specific details on our "portfolio" of debt. (We're also a fair bit larger than most startup dev teams, so having this level of formalism is more appropriate in our case than say just a whiteboard somewhere...)
I would love to know your formal approach (or as close to it as possible). I personally see technical debt as debt to be leverage but I lack the means to track it so that we are always aware of how much debt we have.
We (or at least I) also think of it as leverage. We also have a very strong 80/20 ethic, so we don't have particular qualms about using the leverage that this debt can provide.
We don't do anything magical; there is no secret sauce, noe no spreadsheets with formulae or anything fancy; it's literally just a series of wiki articles and Jira tickets with issue type "Debt" so we can easily find the documented debt and make plans when/whether to retire it.
So the concrete formal mechanism is "use your bug tracking system and flag them somehow so you can filter/search for them."
I will add some additional links that our top-level debt page references as useful: