I do not know how easy it may be for a current developer such as TeXtidote to offer Grammarly as an alternative to Language Tools
perhaps you could raise a feature request at https://sylvainhalle.github.io/textidote
Looking through the issues raised there it is unlikely unless Grammarly changes significantly.
1) It appears that whilst I can open a local tex file or report.html or md file from the command line in Grammarly Desktop and it will allow me to make changes, The TeXtidote developer finds the browser extensions are not accessible unless tex reports are physically online !
2) Both offer overlapping and similar functions, However Grammarly does not see anything near as much out of place in a TeX file than the more format dedicated TeXtidote.
I suggest you look at this as a TeX specific alternative solution.
To see how easy it is to add a suitable editor script to any TeX editor see my "Out Of Box" example here (yes I know screenshot is not Mac TexShop however TeXtidote is cross platform (java), so it should work on any TeX editor with the correct shell command.