Text chat comes with different channels including the whole zone, just the small area around you, your guilds, a temporary channel for your group while you’re in one (which you will know when it happens), and a way to have a one-on-one private conversation with a specific person. You can adjust your chat window to only show certain channels. For example I have a window that only shows the Chorrol guild chat for when I want to tune out everyone else who is playing but still want to see if a Chorrolite needs help or wants to go do something fun. People who are doing a serious RP tend to use a private text chat channel (guild, group, or whisper), go to someone’s house where they won’t be disturbed by random people, or use one of the less busy public channels. This will probably not make sense until you are playing, but it will make perfect sense then.
In the early days of Playstation voice chat I always turned it off as soon as I entered a zone because it was a noisy mess of fools and background noise from open mics. I haven’t played on PS4 in a while, so I don’t know if it’s better. As Acadian said, voice chat is not built in to the PC ESO experience, so you’ll only have to speak out loud and hear people who you’ve chosen to interact with on their Team Speak or Discord (or whatever) channel. And you will not find me trying to imitate Jerric’s voice on there.
Sometimes you will find a bunch of people standing around in an out of the way place, looking like nothing is happening. They are probably setting a private channel on fire with their RP. This happened to Jerric outside a chapel in I think Bangkorai. A guy was standing on the steps in a hands-behind-back commander pose, facing a whole group of people. Jerric had a quest inside the chapel. So he walked up and stood at the edge of the group to see if anyone was going to tell him something. All was quiet, so he walked up around the side of the group and behind the commander to go into the chapel. There was nothing to stop him from running straight through the middle of them except that he is not a jerk. RP in the wild can get disrupted by random people.
There are apparently places that people go for pickup RP, I think one is a tavern in Riften? And lots of guilds who organize events. My Orsimer furniture maker Pog got zone-chat invited to a wedding once, which was fun. The actual vows and whatnot were on a private chat that he couldn’t see, but quite the party broke out in zone chat afterward.