No. The typical Just Play player has not played properly in years, knows the rules roughly rather than exactly, and is coming back to it in their thirties. You are the normal case here, not the exception.
The honest version: you will be sore after the first game, and you will have your breath back by about week three. That is it. Nobody is going to say anything about your fitness, because half the team is in the same position and the other half was last season.
Why the format helps
Squads are deliberately bigger than the side that takes the court, so there is a bench and people rotate through it. A basketball squad is 8 or 9 for a game with 5 on court.
Substitutions are expected, not a favour you are asking for. Call for a change and you get one. See Substitutions: how do subs work, and can I bring a fill-in?.
Games are short. Most run under an hour, once a week.
Choosing social rather than competitive in your player survey puts you with people who want the same thing you do.
If you want to ease into it
Book a single game before committing to a season. The price is shown on each game listing, you turn up once, and if it is not for you there is nothing to cancel. Have a look at One Game, or read Seasons or One Game: which one should I pick?.
Some sports are kinder to a rusty body than others. Volleyball and netball involve less continuous running than futsal, 5-a-side or touch. If you want to start gently, start there.
One genuine word of caution
We organise social sport, we are not a medical service, and Just Play does not provide injury cover. If you have a heart condition, a recent injury, or you have been told to take it easy, speak to your GP before you sign up rather than after. Warm up properly, and tell your team when you need to come off.
Still need a hand? Have a look at what is running near you on the Just Play website.