Yes, the y2k crisis was real, or more accurately, would have been a serious crisis if people had not rushed and spent lots of money to deal with it ahead of time. In many systems it would have been no big deal if unfixed, but there were a huge number of really important systems that would have been a serious problem had they not been fixed. Part of the challenge was that this was an immovable deadline, often if thing…
For example, at a former employer of mine, a big justification for getting rid of the IBM-compatible mainframe and a lot of legacy systems which ran on it (various in-house apps written in COBOL and FORTRAN) was Y2K.
In reality, they probably could have updated the mainframe systems to be Y2K-compliant. But, they didn't want to do that. They wanted to dump it all and replace it with an off-the-shelf solution running on Unix and/or Windows. And, for reasons which have absolutely nothing to do with Y2K itself (the expense and limitations of the mainframe platform), it probably was the right call. But, Y2K helped moved it from "wouldn't-it-be-nice-if-we" column into the "must-be-done" column.