Should have past participle

Hello.

I'm learning English as a second language.

I need your help.

I was taught that ' should have past participle' is used to talk about things we regret.

It is highly appropriate that Dr Samuel Johnson should have published his Dictionary at the very beginning of the heyday of the middle class.

In this sentence, dose it contain the meaning of regret like ' I should've gone to bed earlier'?

Could you please paraphrase the sentence?

Thank you in advance.