When using the Text Editor to post anywhere on the site (Forums, Blogs),

Under the Tools tab, there isn't an option for Spellcheck.

As the Browser Automatic Spellcheck is not engaged on the Text Editor, it is impossible to have a spellcheck system on HEE and it must be done offsite.

Grammarly is working just fine for me, but I'll have to see about the browser's spellchecker

Not a bug. This is no longer a feature of the free editor. It's a pay feature only.