Check if allow re entrance is unchecked. If that's the case, profiles on qualifying into the segment, the second time, will not enter the journey. Also, check the type of segmentation - if its streaming or batch.

You can refer to this thread where a similar question was posted https://experienceleaguecommunities.adobe.com/t5/journey-optimizer-questions/can-i-update-profile-or-trigger-event-using-restful-api/m-p/657183#M1530 

It would be on the following lines -  1) Create a unitary event (say for example - eventType = 'commerce.checkout')2) Create another unitary event (with eventType = 'commerce.purchases') and specify a time out say for 1 hour. If you don't see a purchase event happening in an hour from the initial ev...

You can follow the pattern mentioned here in this documentation https://experienceleague.adobe.com/docs/journey-optimizer/using/orchestrate-journeys/journey-use-cases/technical-use-cases/limit-throughput.html?lang=en to limit the throughput using a combination of splits and percentages 

Can you increase the timeout to 30 seconds in the journey properties and see if its still the same case ?  

Once the targeted user clicks on the list unsubscribe header marketing.email.val gets updated to 'n' under the consents.idSpecific... objectThis information is available in profile snapshot system dataset which can be exported to cloud storage destinations.Reference -  https://experienceleague.adobe...

Check if the testProfile attribute is set to true and also, if the namespace in the read segment node is matching with what is there on the test profile record.

If you find both of these audience membership correctly showing up against the profile you are looking for, that should be a good validation. You can also query the dataset and find out the exact profiles that landed in it. Reference on profile samples -  https://experienceleague.adobe.com/docs/expe...

Did you try directly using the collection managements functions by overriding the push parameters ? You will have to override all the three parameters, ensuring the appId and token are specific to apns/fcm.     

You can refer to this thread where a similar ask was posted https://experienceleaguecommunities.adobe.com/t5/journey-optimizer-questions/can-i-update-profile-or-trigger-event-using-restful-api/td-p/657183