When I was learning Spanish (on my own) 25 years ago I had a Spanish/English dictionary. It only translated verbs to Spanish infinitive, but each had a numerical index mapping it to a class of verbs with the same conjugation pattern.

There was a section at the front of the dictionary with full conjugation patterns over all tenses for one sample verb in each class.

Eg, each type of stem-changing verb fell into one index, full irregulars were singletons in their own class, some irregulars that behave similarly (iirc tener and detener) shared one class.

So all verbs in Spanish fell neatly into a few dozen unique patterns, and the indexing was already done.

I was going to build a quiz software just like you mentioned to conjugate any verb in any tense, but “never got around to it”.

I wonder how the reverse-string trie pattern in the article would be for reconstructing the class mapping.