(1) The restaurant served the special lunch menu starting April 1, 2020.
(2) The restaurant has been serving the special lunch menu starting April 1, 2020.
I am not sure which tense of "serve" is correct. Please help me. Thank you.
"Starting" is tripping you up. That's for the future. The restaurant will be serving it starting whenever.
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"Starting" is tripping you up. That's for the future. The restaurant will be serving it starting whenever. You mean "since", "The restaurant has been serving the special lunch menu since April 1, 2020." or "first", "The restaurant first served the special lunch menu on April 1, 2020."
You definitely want (2).
Use the present perfect continuous whenever an action started at some time in the past and continued since then and still continues to present time.
I/you/we/they have been -ing
he/she/it has been -ing
They've been gardening there for years.
We've been rehearsing the play all week.
Food prices have been going up for decade