I don't think Springer is eligible
There aren't any actual rules on who can and can't play in summer league. It tends to be mostly first and second year players, with an occasional third year player. I doubt Springer would go since he's entering his 4th year, but there's no rule barring it.
Everything I've seen written about it, says it is for 1st and 2nd year players (and I believe that is NBA contract so 2-way guys get some extra time). I can't recall a 3rd year player that was a 1st round pick ever playing in summer league (perhaps a situation like Holmgren or Embiid where a guy misses a full year or two). And Springer will be in year 4. He may be the type of player that could benefit, so we will see if he is on the team, but if I was to bet on it, I'd take the no he won't play.
There are no official rules about eligibility. The Celtics had a bunch of third-year guys a couple of summers ago: Romeo Langford, Carsen Edwards, and Bruno Fernando were all heading into year three, and Langford was a former lottery pick even, with the other two early 2nd-rounders still on their rookie deal.
Summer league is not required for any player. Teams recommend players go, and most of the time they agree. Sometimes players ask to go. My guess is Springer will not play but will head there for some workouts/practices to keep developing over the summer (Grant Williams did that the same year Langford et al played heading to year 3).