I think 覚える itself mostly refers to the action of remembering itself, so if you want to say I have will memorized that you can say 覚えている for “I remembered that, and now am in a state of having remembered”.
Take this example sentence from Bunpro for example:
I still haven’t memorized them/it all, but I will definitely have them/it memorized by next week.
When speaking in the present tense it uses 覚おえている (I haven’t remembered that), but when speaking about changing that it uses 覚える since we are talking about the actual action of committing the information to memory and not the action of recalling it later.
Although I don’t have evidence to back it up I would expect 覚えた might be used if we were trying to say something like “Last night I memorized some new words” or something where we’re referring to the act of memorizing in the past tense, rather than recalling in the present.