<h1> is for first level, <h2> for second level down to level 6.
If you want to change <h2> into <h3> use the following regex:
search:
replace:
options: minimal matching, search in all html files
but be careful: if you want to change now all old h3 to h4 you cant cause you have now new h3 which will be converted to. So you have to start at the bottom going to the top when changing the levels in more then one hierarchy.