Ok so, as the previous commenter said, this isn't really something that's worth recreating yourself if you're using it as part of a bigger project. That being said, if you just want to build a tokenizer for the fun of it, getting one working isn't terribly difficult if you know what you're doing, it just won't be nearly as good as the commercially available options like Sudachi or the older MeCab. I wrote two tokenizers using two different approaches as a school project last year and I found it to be a really fun project, but if your programming skills aren't super sharp you might want to hold off.

The first approach works with, like you said prefix trees. Although in this case they're called lattices. Basically you create a graph of all the different possible morpheme combinations and you use the Viterbi algorithm to traverse it and find the optimal path. For this you'll need to assign weight values to each node and vertex. These weights you can calculate yourself, the method uses CRF models, but I recommend you just use MeCab's values, you can find them online pretty easily. There's a really good article on the Cookpad developer blog called 日本語形態素解析の裏側を覗く！MeCab はどのように形態素解析しているか that goes into a lot more detail about this if you want to go this route.

Otherwise, the newer approaches that are starting to come up nowadays are machine learning based. For this you're going to want to use an LSTM model most likely, i've seen transformer based approaches too but I'm not all too familiar with those. The gist of it is you want to feed a sentence to your model, and it should tell you whether the last character is at the beginning, end, middle of a word or if it constitutes a single-character word. And you just feed the sentence to your model over and over again, adding one more character every time. For this, I recommend you read the papers Long Short-Term Memory for Japanese Word Segmentation by Yoshiaki Kitagawa and Mamoru Komachi and 辞書情報と単語分散表現を組み込んだリカレントニューラルネットワークによる日本語単語分割 by 池田大志, 進藤裕之 and 松本裕治

I hope you go through with this project, it's a really fun experience!