I compiled a list of all widget methods that return 'None' and for which it _could_ make sense to make this change.
(I filtered out some methods, like watch and action methods.)

I tried choosing a subset of those methods, trying to only pick methods for which there weren't two things that could be returned (e.g., 'Widget.move_child' _could_ return either the widget or the child that was moved) and I also tried to only pick methods that have little or no parameters (e.g., 'Widget.animate' has many parameters and is typically called with quite a few.

These are all the 'Widget' methods for which this could make sense:
- 'move_child' (either return 'self' or the actual 'child' that was moved…)
- 'animate'
- 'scroll_to' / 'scroll_relate' / 'scroll_home' / 'scroll_end' / 'scroll_left' / 'scroll_right' / 'scroll_down' / 'scroll_up' / 'scroll_page_up' / 'scroll_page_down' / 'scroll_page_left' / 'scroll_page_right' / 'scroll_visible'
- 'refresh'
- 'focus' / 'reset_focus'
- 'capture_mouse' / 'release_mouse'

Additionally, I looked at each widget, and found these methods:
- 'Tree'
    - 'TreeNode'
        - 'expand' / 'expand_all' / 'collapse' / 'collapse_all' / 'toggle' / 'toggle_all'
        - 'set_label'
    - 'clear' / 'reset'
    - 'select_node' (either return 'self' or the actual 'node' that was selected)
    - 'scroll_to_line' / 'scroll_to_node'
    - 'refresh_line'
- 'ToggleButton'
    - 'toggle' (and 'action_toggle'?)
- 'TextLog'
    - 'write'
    - 'clear'
- 'Tabs'
    - 'add_tab' / 'remove_tab'
    - 'clear'
- 'Switch'
    - 'toggle' (and 'action_toggle'?)
- 'Static'
    - 'update'
- 'Pretty'
    - 'update'
- 'Placeholder'
    - 'cycle_variant'
- '_markdown.py'
    - 'MarkdownBlock'
        - 'set_content'
    - 'MarkdownTableOfContents'
        - 'set_table_of_contents'
- 'Input'
    - 'insert_text_at_cursor'
- 'DirectoryTree'
    - 'load_directory'
- 'DataTable'
    - 'update_cell' / 'update_cell_at'
    - 'clear'
    - 'refresh_coordinate' / 'refresh_row' / 'refresh_column'
    - 'sort'
- 'Button'
    - 'press'

Related issues: #1908
Related discussions: #1817

Related review comment: https://github.com/Textualize/textual/pull/2102\#pullrequestreview-1354201387