Based on your description of wanting to capture the connections between an application and a database, I would agree that both the Data Extensions (defined in Chapter 34.4.4) and Infrastructure Consolidation Extensions (defined in Chapter 34.4.5) are appropriate. Specifically, two of the purposes of the Data Extensions is to capture the "creation of physical data components that implement logical data components and are analogous to databases, registries, repositories, schemas, and other techniques of segmenting data" and the "creation of data lifecycle, data security, and data migration diagrams of the architecture to show data concerns in more detail". Some of the purposes of the Infrastructure Consolidation Extensions are to capture "creation of logical and physical application components to abstract the capability of an application away from the actual applications in existence" and "creation of logical and physical application components to abstract product type from the actual technology products in existence".
If you were to fully create both of these extensions, you would need to create the following diagrams:
- Data Security diagram
- Data Migration diagram
- Data Lifecycle diagram
- Process/Application Realization diagram
- Software Engineering diagram
- Application Migration diagram
- Software Distribution diagram
- Processing diagram
- Networked Computing/Hardware diagram
- Communications Engineering diagram
All of these diagrams are defined in Architectural Artifacts (Chapter 35).
Based on the drawing in your question, the Software Distribution Diagram and Networked Computing/Hardware Diagram most closely matches that. The Software Distribution diagram shows application structure and physical distribution across physical pieces of technology and geographic location. The Networked Computing/Hardware diagram shows the logical connections between components of the application. Since you also mention updates to applications and databases (I'm interpreting that to be a deployment of a new version or a technology refresh to a new vendor), the Application Migration Diagram seems appropriate as well as it shows how you intend to move from the baseline versions of components to the target version across all of the environments. It should be noted that all of these fall under the Infrastructure Consolidation Extensions.
Looking at the full definitions of these diagrams (and glancing through the definitions of the other diagrams), TOGAF never specifies a particular modeling notation or technique. Each of the TOGAF Extensions describes a particular facet of architecture, a set of models that help you capture information relevant to that facet of architecture, and gives specific names to diagrams that serve specific purposes.
If you must comply with TOGAF standards, the best thing to do would be to choose your Extensions (it looks like you have), ensure that the purpose aligns with what you are trying to communicate, look at the list diagrams that support that extension, then look at the intent and purpose of those diagrams. Then, work with stakeholders who will be using the documentation (it's not just the diagrams - there is likely to be text, tables, and other information) associated with that Extension.
Another recommendation that I have comes from IEEE Standard for Information Technology -- Systems Design -- Software Design Descriptions (1016): the use of standardized design languages is preferable to other design languages. The idea if you are using a standardized design language (and using it properly), then you do not need to explain what your notation means to readers. If you are not using a standardized design language or using symbols from a standardized design language in a non-standard way, you need additional content to explain to readers how to interpret your diagrams and design notations, which leads to a more verbose architectural or design description.
In short: First, consult with your stakeholders. Find out what diagrams and models would be easiest for them to understand and use. There may be organizational standards or conventions already in place. If there is no standard, convention, preference, or consensus, seek out a standardized notation that can be used to communicate the information that the diagram is intended to communicate. If there is no standardized notation, then you can choose to use a notation of your own devising as long as you also make it clear to a reader how to understand that notation.