You can integrate the productivity services in SharePoint Online with on-premises SharePoint Server 2019 by using a SharePoint Server 2016 hybrid environment.

A SharePoint Server 2019 hybrid environment is based on trusted communications between SharePoint Online and SharePoint Server 2016. When you have established this trust framework, you can combine an on-premises SharePoint Server deployment with a SharePoint Online cloud solution and deliver a consistent user experience across a combined environment. For example, you can use the unified search capability to search across both parts of a hybrid solution (on-premises and online) by using a single search query.

Hybrid environments are helpful when it is not possible for an organization to fully migrate its SharePoint deployment to the cloud due to business, technical, or other reasons.

For example, there might be a compliance or data sovereignty policy in your organization that requires data to be hosted in a particular location. By using the hybrid model, your organization can start to achieve the benefits associated with the use of a cloud solution while at the same time continuing to use an on-premises deployment that provides the data governance and customization flexibility you require. By using a hybrid solution, your organization can achieve a higher degree of flexibility than you would have achieved if you forced a choice between an on-premises model or a cloud model. For users, the hybrid model is mostly transparent.