An enterprise geodatabase is the only option that meets both requirements. It is specifically designed for a multi-user environment, allowing simultaneous editing from various clients, including web and mobile applications, via feature services. It is built on a commercial relational database management system (RDBMS) such as SQL Server, Oracle, or PostgreSQL. This architecture allows a database administrator (DBA) to perform advanced performance tuning, such as creating and managing database indexes on the feature class business tables to optimize common queries, which directly aligns with the scenario's requirements.

B. File geodatabase: This is a single-user editing model. While multiple users can read the data, only one user can edit at a time, making it unsuitable for concurrent editing by web and mobile apps.

C. Mobile geodatabase: This is based on SQLite and designed for single-user, offline workflows on mobile devices. It is not intended to serve as a central, multi-user database for simultaneous editing.

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1. Esri, ArcGIS Pro Documentation, "Types of geodatabases." This document explicitly states, "Enterprise geodatabases... are stored in a relational database... can be edited simultaneously by multiple users... [and] are required for some multiuser geodatabase capabilities such as versioning, archiving, and replication." This supports the multi-user editing requirement.

Source: https://pro.arcgis.com/en/pro-app/latest/help/data/geodatabases/overview/types-of-geodatabases.htm

2. Esri, ArcGIS Enterprise Documentation, "What is an enterprise geodatabase?" This source clarifies the role of the underlying RDBMS: "They take full advantage of the underlying DBMS architecture to support... a large number of simultaneous users... [and] a relational database that can be scaled to meet the needs of the organization." This confirms its suitability for DBA management and performance scaling.

Source: https://enterprise.arcgis.com/en/portal/latest/use/what-is-an-enterprise-geodatabase-.htm

3. Esri, ArcGIS Pro Documentation, "Attribute indexes." This page details how indexes are managed across geodatabase types. For enterprise geodatabases, it notes, "When you create an attribute index for a feature class or table in an enterprise geodatabase, a corresponding index is created in the database." This directly links the DBA's task of adding indexes to the enterprise geodatabase structure.

Source: https://pro.arcgis.com/en/pro-app/latest/help/data/geodatabases/manage/attribute-indexes.htm