vim-LanguageTool VS Emacs-langtool

I do not think any spellchecker can do this, as a spellcheck is for checking only spelling. You probably is looking for grammar tools. I cannot say which is the best, but there is. e.g, this one: https://github.com/dpelle/vim-LanguageTool

I've been trying to utilize Vim to do more writing so I tried to install LanuageTool and a related vim plugin: https://github.com/dpelle/vim-LanguageTool/

Yes. You can build the command-line application Java Jar from that repo. I also combine it with vim (https://github.com/dpelle/vim-LanguageTool).

Language Tool does this, I believe, but I think it's modal rather than on-the-fly.

Perhaps something like https://github.com/mhayashi1120/Emacs-langtool which you can self host. Or if you don't mind SaaS - there's grammarly integration for emacs too.

There’s already Emacs package, but it works only with offline version.

https://github.com/mhayashi1120/Emacs-langtool

Now that I checked, looks like there’s another package, but I didn’t t try it.

https://github.com/emacs-languagetool

Check out textidote too. It's languagetool understanding \LaTeX syntax, and you can set it for flycheck-checker. Emacs-langtool coupled with langtool-ignore-fonts is also good for \LaTeX documents. You may want to configure them to disable a few rules to reduce false positives.

I use https://github.com/mhayashi1120/Emacs-langtool

Didn't see it so far: LanguageTool integration in Emacs. It really helps me a lot, as I'm a making lot of language errors. LanguageTool requires Java (standalone app is a Jar file), could start is a bit long, but then it's really easy to use and for me feedback is better integrated in Emacs than for example in LibreOffice.