So I realised my first try above did not take indentation into account. Here is the snippet I came up with. It's good enough for my purpose. So far, in spite of the limitations described below, I've been able to use it in a satisfactory manner.

[
  {
    "key": "alt+shift+a",
    "command": "editor.action.insertSnippet",
    "args": {
      // Indentation-saving snippet
      // MATCH
      // ^                Beginning of selected text
      // ( *)             $1 is a possible indentation that is to be reused for delimiters and content
      // ('''\n *)?       $2 is a possible opening delimiter, including following line break and indentation
      // (.*?)            $3 is a possible content (non-greedy)
      // (\n *''')?       $4 is a possible closing delimiter, including previous line break and indentation
      // $                End of selected text
      // SUBSTITUTION
      // $1               If there was an indentation, indent the opening delimiter
      // ${2:?\n:'''\n}   If there was an opening delimiter, replace it with a line break, otherwise make a delimiter and line break
      // $1               If there was an indentation, indent the content
      // $3\n             The content and a line break
      // $1               If there was an indentation, indent the closing delimiter
      // ${4:?\n:'''}     If there was a closing delimiter, replace it with a line break, otherwise make a linebreak and a delimiter
      // LIMITATIONS
      // The selection must be the entire lines of the content to comment in / out
      // Line breaks are created because we can't replace a group by nothing in this REGEX implementation
      "snippet": "${TM_SELECTED_TEXT/^( *)('''\n *)?(.*?)(\n *''')?$/$1${2:?\n:'''\n}$1$3\n$1${4:?\n:'''}/s}"
    },
    "when": "editorTextFocus && editorHasSelection && editorLangId == 'python'"
  }
]

My settings generate indentation as spaces, but I assume it could be adapted to tabs.

I'm accepting @rich neadle's reply as the answer, namely this did answer the initial question:

I am not aware of if-else if-else if-else then replacements that I could build with regex