wrote:
Shortly after I was level at 4000, I was cleared to
intercept localizer.

No you weren't, you were instructed to intercept the localizer.

I climbed back to 4000 and about 30 seconds later, was
cleared to decent.

No, you were instructed to descend and then cleared for the approach.

I did not think about it at the time, but does clear to intercept
localizer mean I cannot decent until I am clear to decent?

You need to discover the difference between a clearance and an
instruction, especially the phraseology ATC uses to issue a clearance.