I'm going to stake a claim here: a main cause of the confusion of the new rules, is that the game has never had any tool for measuring VP during skirmishes.
The only way so far, has been if you happen to have won one of those scoring dials that were included in a few of the tournament kits. I've seen the book-keeping done with anything from the threat/round dial to objective tokens, to strain tokens, to a piece of paper, or a phone app.
The reality is, though, that there are so many things that add and subract victory points in the game, that it is getting harder and harder to represent the points with anything but a piece of paper or the app used (or the elusive dial). If there had been some sort of component for book-keeping in the base game, we wouldn't need all sorts of spurious ways of keeping track of them - strain on deployment cards for reinforced figures here and singular points from On A Diplomatic Mission there, or points from Pickpocket over there. Instead the rules would just tell us to X number of points to your tracker.
This is exactly correct.
And to add further, the tournament rules specifically restrict taking notes, which puts pen and paper scoring in a hazy grey area.
Score Dial or Phone App is the best way. It should be official. Mind you the prize kits dials are horrible.
The threat/round dial is the clearest and easiest "semi-official" way.
The rules forbid not only taking notes, but also 'consulting outside material'. Players can only 'reference' 'official rules documents' and 'game components containing non-hidden information'.
Since neither a scoring dial or a phone app is a 'game component' ('game components' are spelled out to be models, cards, dice, tokens and map tiles), it is just as illegal to use them as it is to take notes.
Which locally we all had a collective laugh about, declared it amusingly idiotic and continued to use dials, notes, phone apps and dice result cheat-sheets at tournaments.
Interestingly, even the damage tracking sheets they were including in tournament kits were technically illegal until they added a paragraph about 'alternative indicators' a while ago. We all had a chuckle about that as well.