At the end of #2802 (comment) you mentioned I should open a new issue for the following:

One issue I had in the past is that I needed a custom autoload/vimtex/view/my_zathura.vim file containing

  if g:vimtex_view_automatic
    "
    " Search for existing window created by latexmk
    "   It may be necessary to wait some time before it is opened and
    "   recognized. Sometimes it is very quick, other times it may take
    "   a second. This way, we don't block longer than necessary.
    "
    if !has_key(self, 'started_through_callback') && g:vimtex_view_xwin_exists
      for l:dummy in range(30)
        sleep 50m
        if self.xwin_exists() | break | endif
      endfor
    endif

Specifically, I changed 500m to 50m, as half a second was too long. Now this same sleep timer is found here:

Currently, without changing the 500m it seems to be fine, but for some reasons in the past I had to change it. If I look at some of my previous issues on here, this comment may have been the original cause #1063 (comment) ... however, I don't remember at this point why exactly I changed it from 500 to 50, it may be that the changes to VimTex since then have made this unnecessary, as I did not notice any significant problems right now.

This is not necessarily an issue anymore, but I am sharing this based on the history that I previously had the issue which required customizing the sleep timer; I am not completely sure if it still matters or not.

Lervag has suggested using timer_start instead of sleep, so perhaps there is yet something to be improved.