In this question we encounter two problems:
One problem is about differences between the single p-value for an anova test in relation to the multiple p-values for a Tukey's range test, for each single contrast. The single contrasts had much lower p-values (regarded insignificant) than the p-value for the single anova test.
One other problem is about a "bug" (which is debatable just abuse of a non-supported feature) in the R-package
car::Anovaregarding the implementation of the
method=brglmFitoption (which it doesn't use for the reduced models). This problem seems to me sufficiently on-topic for this website. It is a bit much about bugs in software but in order to tackle it, it does help to have some statistics knowledge.
The question was initially written rather confusingly, but currently it is in a state that you can reproduce the problem(s).
Now the problem from the point of view of a person on stackexchange that wants to answer/solve/help this problem (these questions) is how to deal with the multiple issues in a single problem? or how to deal with complex problems?
On the one hand: answering such questions can be simple.
(Which, for the specific example, I currently did in comments. But I was left wondering how to make those comments in an answer or what to do with the question.)
But on the other hand: it may be important to correct such questions, cut it down into smaller portions, such that they also remain valuable in the future as part of an easy search-able database of questions.