Yes, you can create your own Patterns and Template Parts in WordPress when using a block theme! Both Patterns and Template Parts can be built using the Site Editor.
Open the Site Editor: Navigate to “Appearance” > “Editor” > “Patterns” in your WordPress dashboard. Click the “+” icon next to “Patterns” in the left sidebar. Choose “Create pattern” or “Create template part” from the options. Build your layout: Similar to the block editor, use the block inserter (+) to add and arrange the blocks you want in your pattern/template part. Style and customize as needed. Once you have finalized your design, click Save.