I think we collectively have skipped an important step in coming up with a notation system, and so we're trying to do 2 things at once. The goal of a notation system is to display relevant information and filter out unneeded information. But we jumped straight into discussions of syntax, without first talking about which information is relevant or not! Thankfully Geronimoo's system, which closely resembles plaintext, seems to have focused the discussion back to this important topic. I suggest we explicitly focus our efforts on that topic before we deal with anything about style.
I think we've all implicitly agreed about one thing that needs to be included in the gamelog: Whenever the player makes a non-trivial decision. However, in order to include this I think a gamelog needs to include not just what actions were taken, but what alternatives were available, as well as significant data gained. This will sometimes require going beyond what actions were taken, and explicitly call out actions that were not taken.
For example, I want to know if terminals collided. This is a big deal when it happens: the player has to make a decision of what to play, they gain knowledge about what actions are still available in their deck, and in general it has a big impact on their mental state. Same thing with, e.g., wasted (targetless) King's Courts, or electing not to play a trashing Action card due to lack of a good target, or not playing 3 copper to buy a Grand Market when Platinums are available. These are player actions available that were not taken, which are as significant as actions that were taken.
I think the hardest thing to include is deck state, and how players manage their reshuffling. Top-level players will be making decisions to play or not play drawing cards based on how many cards are in their deck, and what they know those cards are. It's hard to reconstruct this information without card-by-card breakdowns of all hands since the last reshuffle, or including deck state annotations where it might be relevant. I honestly have no idea what to do about this.