Is being “invited to” an interview the same as being “invited for” one?

Solution 1:

"Invite," in the sense you're using it, takes the preposition "to."

"To" connotes the appointment, meeting, opportunity, etc. to which one is invited: The Queen invites Belle to the Jubilee Dance.

When one uses "for," it's a more colloquial sense connoting what one might be enjoying, consuming, etc.: The Queen invites Belle to Windsor Castle for bagels and lox.

Or: Adam received a gift of rare Scotch, and invited me for a taste.

The confusion you're understandably having is that the interview is both an occasion and something of a benefit or an honor.

"Invite for" is colloquial, again. People say things like "My boss invited me to his house for drinks." That illustrates the difference. "My boss invited me to his house" but "My boss invited me for drinks." The second sentence is colloquial. Thus, in your LinkedIn post, use "invited to an interview," as you're describing an occasion, meeting, or date.