Until when can I stay in Thailand on a tourist visa with a multiple entry?

Okay you're confusing the visa validity with the entry stamp you get when you enter on that visa :/

Your visa is valid until April 23 <- meaning as long as you enter the country on or before that date you'll get stamped in for 60 days.

Right now seeing as you entered on the 3rd of April you were given a 60 day stamp until 1 June <- that's how long you can stay here.

Remember you can also get a 30 day extension on that 60 day entry stamp you have for 1900baht a the immigration office