According to these lines, the script only gets triggered if you go to a link which follows with "anime/" and "manga/".
Now the problem is -> When you go to the front page in the first place (anilist.co/) and then click on a anime or manga page, the script doesn't get triggered because of the fact that the script still thinks that you are on "anilist.co/". To solve the problem, you need to refresh the anime or manga page and due to the refresh the script gets triggered.
To solve this issue, i recommend to add a new line to your script:
Found a bug
// @match https://anilist.co/anime/* // @match https://anilist.co/manga/*
According to these lines, the script only gets triggered if you go to a link which follows with "anime/" and "manga/". Now the problem is -> When you go to the front page in the first place (anilist.co/) and then click on a anime or manga page, the script doesn't get triggered because of the fact that the script still thinks that you are on "anilist.co/". To solve the problem, you need to refresh the anime or manga page and due to the refresh the script gets triggered.
To solve this issue, i recommend to add a new line to your script:
// @match https://anilist.co/*
so now the script always gets triggered and you dont have this annoying issue anymore.