Start with default generated template

templates/user/user.html.twig

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+{#
+/**
+ * @file
+ * Theme override to present all user data.
+ *
+ * This template is used when viewing a registered user's page,
+ * e.g., example.com/user/123. 123 being the user's ID.
+ *
+ * Available variables:
+ * - content: A list of content items. Use 'content' to print all content, or
+ *   print a subset such as 'content.field_example'. Fields attached to a user
+ *   such as 'user_picture' are available as 'content.user_picture'.
+ * - attributes: HTML attributes for the container element.
+ * - user: A Drupal User entity.
+ *
+ * @see template_preprocess_user()
+ */
+#}
+<article{{ attributes.addClass('profile') }}>
+  {% if content %}
+    {{- content -}}
+  {% endif %}
+</article>

templates/user/username.html.twig

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+{#
+/**
+ * @file
+ * Theme override for displaying a username.
+ *
+ * Available variables:
+ * - account: The full account information for the user.
+ * - uid: The user ID, or zero if not a user. As used in anonymous comments.
+ * - name: The user's name, sanitized, and optionally truncated.
+ * - name_raw: The user's name, un-truncated.
+ * - truncated: Whether the user's name was truncated.
+ * - extra: Additional text to append to the user's name, sanitized.
+ * - profile_access: Whether the current user has permission to access this
+     users profile page.
+ * - link_path: The path or URL of the user's profile page, home page,
+ *   or other desired page to link to for more information about the user.
+ * - homepage: (optional) The home page of the account, only set for non users.
+ * - link_options: Options to set on the \Drupal\Core\Url object if linking the
+ *   user's name to the user's page.
+ * - attributes: HTML attributes for the containing element.
+ *
+ * @see template_preprocess_username()
+ */
+#}
+{% if link_path -%}
+  <a{{ attributes.addClass('username') }}>{{ name }}{{ extra }}</a>
+{%- else -%}
+  <span{{ attributes }}>{{ name }}{{ extra }}</span>
+{%- endif -%}