'Would' in this sentence is actually the past-future tense in English indicating someone was going to do something, other than politeness or the conditional usage coming with a clause, which is equivalent to le conditionnel présent in French. However, since the temporal adverb is just 'souvent' which means 'often', it's more natural to translate as 'used to tidy up' than 'would tidy up'.
Another context would allow for a past-future tense with would: "You knew I would tidy my room." In French, you would also need a conditional present "Tu savais que je rangerais ma chambre".
But this sentence is not suitable for a past-future tense and again "[past trigger: see above examples] + I would tidy up my room" is the expression of a past habit.
Yes, but I'm still distinguishing them. Think of the will in I will always love you. and then rewind will to the past and it becomes I would always love you.. I would often tidy up my room. sort of sounds like I would often like to tidy up my room. or I was often willing to tidy up my room. which includes some subjective will, while I often tidied up my room or I used to tidy up my room merely talks of the objective fact.
This answer should be accepted because in AmE it is extremely common to have to "clean your room" when the implied meaning is "tidy your room". I'd say that's the most common way to say this -- I've actually never heard anyone I know in the U.S. use 'tidy' as a verb, and they rarely even use it as an adjective. I just checked with my mother and she agrees that she never uses the word 'tidy', only 'clean', or less often 'clean up', or even 'straighten up'.
It's grammatical even when there's no context, yet I just don't find it necessary here. It would be totally understandable if Duo wanted to demonstrate the difference between would tidy up and rangerais, the latter one being only good for use in a conditional clause. Otherwise it should not be the most plausible translation without proper temporal adverbials such as after work or on Sundays, the same way I won't translate Je range souvent ma chambre into I will often tidy up my room even though it's 100% grammatical.