It sounds like you've really connected with the characters and story of the series you're referring to, and it's not uncommon for stories to have that effect on people. When a series ends, especially when you've become so invested in it, it can leave a void. However, the beauty of storytelling is that it often sparks creativity in others. While official continuations or expansions may not exist, there's a vibrant fan community out there that may have created fanfiction or other fan works to continue the story or explore different aspects of it.
If you haven't already, you might try searching for fanfiction or fan-created content related to the series. You may find something that scratches that itch for more adventures with Onizuka and the Class of 4. Additionally, sometimes creators release supplementary materials or side stories, so it's worth checking if there are any official spin-offs or extra content related to the series.
Regardless, it's wonderful to hear how much the series has impacted you and brought you joy. Sometimes, the best stories are the ones that leave us wanting more, as they inspire us to imagine our own adventures and endings for the characters we've grown to love.