The mark, then the situations.
When I look at an identity, I look for what makes it recognisable beyond the logo. Type, proportions, colour and image framing all contribute.
I find it useful to test those choices in very different formats. A large format offers space. A small one forces a decision about what matters. Both are part of the same work.
Coherence shows in repeated details.
Two buttons that do the same thing should behave the same way. A margin chosen in one place needs a reason to change elsewhere. Those repetitions are where an identity starts to hold together.
That leaves room for images and projects with their own character. Shared landmarks make this variety easier to follow.
Consider what will be added later.
An identity needs to accommodate a longer title, a portrait image or content that was not anticipated. I want to understand what stays fixed and what can adapt.
For a website, this also concerns editing: who changes the images, writes the copy or adds a page? A visual direction becomes stronger when it can continue to work through these ordinary actions.