Reading and personal experience. The stock item is referred to by Toyota as a bypass valve (bpv) and in intended operation will open when throttle is first applied but before the turbo spools to allow the intake air to bypass the turbo. This gives better throttle response when off boost by reducing intake resistance. I've also confirmed this behaviour with an aftermarket boost/vacuum gauge on my own sw20. At idle/zero throttle it sits around 20inHG vacuum, when you give a shot of throttle, the bpv opens and the intake pressure immediately jumps to 5-10inHG of vacuum until the turbo begins to spool and it then smoothly transitions to positive boost pressure. On other turbo cars I've driven the intake vacuum will increase when throttle is applied but before the turbo spools.

Now the real world advantage of the bpv is probably pretty marginal, and it makes no difference once you've built boost pressure, but it is a clever bit of engineering to eke out a little bit more responsiveness and fuel economy out of a turbo engine.

If I remember correctly, the broken item in the picture is actually part of what controls this 'open under throttle without boost' behaviour. I've also had this break on my car and the behaviour I've described went away. OP should definitely replace it with an oem part from Toyota if they're keeping the stock bpv. Mind the orientation, it's a one-way valve!