It's currently only possible to use the username and app password or OAuth access token as the credentials for authentication for the search for code API endpoints.

This feature request is to implement the ability to use Workspace Access Tokens (WAT) for authentication in the following endpoints : 

• https://developer.atlassian.com/cloud/bitbucket/rest/api-group-other-operations/#api-workspaces-workspace-search-code-get
• https://developer.atlassian.com/cloud/bitbucket/rest/api-group-other-operations/#api-teams-username-search-code-get
• https://developer.atlassian.com/cloud/bitbucket/rest/api-group-other-operations/#api-users-selected-user-search-code-get