In the below code, there is a simple, very efficient and well tested answer to this question. The code has comments explaining everything in it.
I promise it's not as scary as it looks - it's actually only 13 lines of  code! The rest are all comments, docs and assertions
def split_including_delimiters(input: str, delimiter: str):
    """
    Splits an input string, while including the delimiters in the output
    
    Unlike str.split, we can use an empty string as a delimiter
    Unlike str.split, the output will not have any extra empty strings
    Conequently, len(''.split(delimiter))== 0 for all delimiters,
       whereas len(input.split(delimiter))>0 for all inputs and delimiters
    
    INPUTS:
        input: Can be any string
        delimiter: Can be any string
    EXAMPLES:
         >>> split_and_keep_delimiter('Hello World  ! ',' ')
        ans = ['Hello ', 'World ', ' ', '! ', ' ']
         >>> split_and_keep_delimiter("Hello**World**!***", "**")
        ans = ['Hello', '**', 'World', '**', '!', '**', '*']
    EXAMPLES:
        assert split_and_keep_delimiter('-xx-xx-','xx') == ['-', 'xx', '-', 'xx', '-'] # length 5
        assert split_and_keep_delimiter('xx-xx-' ,'xx') == ['xx', '-', 'xx', '-']      # length 4
        assert split_and_keep_delimiter('-xx-xx' ,'xx') == ['-', 'xx', '-', 'xx']      # length 4
        assert split_and_keep_delimiter('xx-xx'  ,'xx') == ['xx', '-', 'xx']           # length 3
        assert split_and_keep_delimiter('xxxx'   ,'xx') == ['xx', 'xx']                # length 2
        assert split_and_keep_delimiter('xxx'    ,'xx') == ['xx', 'x']                 # length 2
        assert split_and_keep_delimiter('x'      ,'xx') == ['x']                       # length 1
        assert split_and_keep_delimiter(''       ,'xx') == []                          # length 0
        assert split_and_keep_delimiter('aaa'    ,'xx') == ['aaa']                     # length 1
        assert split_and_keep_delimiter('aa'     ,'xx') == ['aa']                      # length 1
        assert split_and_keep_delimiter('a'      ,'xx') == ['a']                       # length 1
        assert split_and_keep_delimiter(''       ,''  ) == []                          # length 0
        assert split_and_keep_delimiter('a'      ,''  ) == ['a']                       # length 1
        assert split_and_keep_delimiter('aa'     ,''  ) == ['a', '', 'a']              # length 3
        assert split_and_keep_delimiter('aaa'    ,''  ) == ['a', '', 'a', '', 'a']     # length 5
    """
    # Input assertions
    assert isinstance(input,str), "input must be a string"
    assert isinstance(delimiter,str), "delimiter must be a string"
    if delimiter:
        # These tokens do not include the delimiter, but are computed quickly
        tokens = input.split(delimiter)
    else:
        # Edge case: if the delimiter is the empty string, split between the characters
        tokens = list(input)
        
    # The following assertions are always true for any string input and delimiter
    # For speed's sake, we disable this assertion
    # assert delimiter.join(tokens) == input
    output = tokens[:1]
    for token in tokens[1:]:
        output.append(delimiter)
        if token:
            output.append(token)
    
    # Don't let the first element be an empty string
    if output[:1]==['']:
        del output[0]
        
    # The only case where we should have an empty string in the output is if it is our delimiter
    # For speed's sake, we disable this assertion
    # assert delimiter=='' or '' not in output
        
    # The resulting strings should be combinable back into the original string
    # For speed's sake, we disable this assertion
    # assert ''.join(output) == input
    return output