You can use Sling Content Distribution to meet the above requirement . This distribute Sling resources between different Sling instances. This can be used to distribute/sync content between AEM Author and Publishers for different scenarios.
"pushing" from Sling instance A to Sling instance B
"pulling" from Sling instance B to Sling instance A
"synchronizing" Sling instances A and B via a (third) coordinating instance C
Also to answer user question, when multiple users submits at same time to different publisher, content will be pulled and synchronized between all the publisher instance.
For more details please have a check on below documents
While there are different ways to store and synchronize user generated data on/between publish instances (@Vaibhavi already pointed out Sling Content Distribution), I would not recommend any of them for actual order data in terms of e-commerce or similar transactional data. AEM and especially the publish tier is not the right place to manage or store transactions and orders.
For online stores, AEM is usually integrated with some kind of e-commerce system (see ), e. g. leveraging the Commerce Integration Framework (CIF) . There are integrations available e. g. for Adobe Commerce (aka Magento)  as well as many 3rd party e-commerce systems.
I would highly recommend to re-evaluate your requirements and check if a different solution approach fits better than storing orders in AEM. As a general rule, storing personally identifiable information (PII) within AEM is recommended to be kept to the absolute minimum and avoided whenever it is possible.
If you have to store order data, I would suggest to leverage an external system (e. g. e-commerce system or in simpler cases maybe a dedicated database) to store and manage this kind of data.