I’ve been in enough jails to say with some certainty: it depends. Like unmagical posted, some places you will absolutely get a phone call at some point. In others, it’s pretty much an ‘executive privilege.’
The truth lies in the squishy, wet world of humanity, not the written word of the law. In one jail I know of, they’d give you three chances to make a free phone call (the other party has to accept, because they can’t let an abuser call the abusee without some warning of who it is), and if they weren’t busy, you would be able to keep trying for a couple of hours. Another place, you might get the phone call, but it could be 18+ hours after you were brought in and you had already seen the judge, been given a personal recognizance bond, and would be delaying your exit from said jail if you made the call. Jailers sometimes like to put the thumb screws to you in any way they can.
Most of the time, inmates will have access to a phone 24/7. Even in solitary, a phone was available. It looked like a pay phone strapped to a dolly that got wheeled right up to the door of the cell and the phone would stick through the little food slot you could look out of. Those phones require money on their account, and it works in a similar manner to the old collect calls. Those phone calls can be as expensive as a dollar a minute. A law was passed in the US around the end of Obama’s term or the beginning of Trump’s that was supposed to set a limit on how much those calls could cost, but I don’t remember what came of it.
The housing I remember in Japan was the coffin box. A little space long enough for you to lie down in, with a small cubby for items. I think it was about 30 sq. ft. and maybe 90 cu. ft.