I found a mention about regex negative lookahead and after breaking my mind I got this regex (assuming you have VALID html tags paired)

// made function a bit ugly just to try to show how it comes together
public function replaceTextOutsideTags($sourceText = null, $toReplace = 'inner text', $dummyText = '(REPLACED TEXT HERE)')
{
  $string = $sourceText ?? "Inner text
  You can find a link here link and a lot 
  of things in different styles. Public platform can appear in bold: 
  public platform, and we also have italics here too: italics. 
  While I like soft pillows I am picky about soft pillows. 
  While I want to find fox, I din't want foxes to show up.
  The text \"shiny fruits\" is in a span tag:  one of the shiny fruits.
  The inner text like this inner inner text  here to test too, event inner text
  omg thats sad... or not
  ";
  // it would be nice to use [[:punct:]] but somehow regex thinks that  are also punctuation marks
  $punctuation = "\.,!\?:;\|\/=\"#"; // this part might take additional attention but you get the point
  $stringPart = "\b$toReplace\b";
  $excludeSequence = "(?![\w\n\s>$punctuation]*?";
  $excludeOutside = "$excludeSequence)"; // note on closing )
  $pattern = "/" . $stringPart . $excludeOutside . $excludeTag . "/im";
  
  return preg_replace($pattern, $dummyText, $string);
}

Example output with default parameters

"""
     (REPLACED TEXT HERE)\r\n
     You can find a link here link and a lot \r\n
     of things in different styles. Public platform can appear in bold: \r\n
     public platform, and we also have italics here too: italics. \r\n
     While I like soft pillows I am picky about soft pillows. \r\n
     While I want to find fox, I din't want foxes to show up.\r\n
     The text "shiny fruits" is in a span tag:  one of the shiny fruits.\r\n
     The (REPLACED TEXT HERE) like this inner inner text  here to test too, event (REPLACED TEXT HERE)\r\n
     omg thats sad... or not     
     """

Now step by step

1. No subsequent matches (if there was only pillowS, we wouldn't need pillow)
2. If the text is followed by any length of \w word symbols, \s spaces or \n newlines and is allowed to end with a start tag Ending punctuation - We don’t need this match, there is a negative lookahead (?![\w\n\s>$Punctuation]*?. Here we can be sure that the match will not go into the new tag because is not in the described sequence ($excludeOutside variable)
The
3. $excludeTag variable is basically the same as $excludeOutside, but applies to cases where $toReplace can be the html tag itself, such as a

Please note that this code cannot overwrite text with or >, and using these symbols may cause unexpected behavior