The most expensive thing in most engineering organizations is re-learning what was already learned. Teams that have to rediscover why a decision was made, or what was tried and didn't work, pay the cost of the original investigation twice. The TPM who writes these things down while they are fresh reduces that cost systematically.
The four things worth capturing are decisions, failures, the current state of constraints, and the people map. Decisions are the most obvious. Failures are the most neglected. The current state of constraints, what is technically possible and what isn't, given the existing system, is what engineers need when they start something new. The people map, who knows what and who you need to talk to before you change something, is what prevents the most painful kinds of surprises.
The format that gets used is the simplest one. A decision log with four columns. A lessons-learned doc that gets updated at each milestone, not just at the retrospective. A constraints doc that lives with the architecture documentation. A stakeholder map that is treated as a living document and not a one-time artifact.
The discipline to keep these updated is the discipline that separates programs that scale from programs that depend on one or two people being present to function. When a key person leaves a program with good documentation, the program loses the person and keeps the knowledge. That is the asset.
Write it while you remember it. The institutional knowledge that lives in the TPM's head is not institutional knowledge. It is personal knowledge with an organization-wide cost.