Vim persists your workspace settings by writing/reading relevant workspace information into/from a session-file. What kind of data gets written into that file is dictated by sessionoptions, the contents of which you can inspect with :set sessionoptions?.
When you enabled the global spellcheck option with :set spell and then had your workspace information saved into the session-file, my guess is that Vim ignored including that global spellcheck option because sessionoptions was not configured to save global options yet. You should verify that by checking whether options(i.e. global options) is listed in the result of :set sessionoptions? and if it indeed is not listed, you can tell Vim to start tracking them by appending options onto sessionoptions with :set sessionoptions+=options. New sessions should contain all global options henceforth. You would probably want to place that command in your vimrc.
.. I want to have my spell checking enabled in one file ...
If you intend to have an option that is only applicable locally e.g. :setlocal spell, you can start tracking localoptions in your sessions with: set sessionoptions+=localoptions.
About vim-workspace — as far as I can tell from it's description, all it seems to do is manage your session-file for you, so you could probably rule it out as a potential source of interference.
