Currently I am using Bitbucket to store the files and branches in Git. Unfortunately, I seem to keep reassociating existing branches with new branches, so where below only the top one should be on the feature/availabilityfix branch, instead it has also associated all the ones below which were/still are on the feature/searchfix branch.
Is it possible to disassociate all those ones from the feature/availabilityfix branch from this other one? I’m completely confused by it!
Also when I merged the previous feature branch back into develop, it has now put that on as a branch for those files. Is that the correct way of dealing with files when merging?

A commit is not “associated” with a branch, it is contained in one (or multiple).
Lets assume you have one branch “develop” which contains commit A. Commit A added file “foo.txt”. You now create a new branch “featureX” based on the latest commit in “develop”.
Commit A is now contained in the branches “develop” and “featureX”. If that wouldn’t be the case, branch “featureX” wouldn’t contain the file “foo.txt”.