Mastodon

There are some accounts that mirror Twitter accounts. I follow one that mirror Woj's tweets, for example.

I don't know what Nitter is, but I think bird.makeup might be what you are looking for.

There are mirrors for most Twitter accounts and I think there is a instance focused entirely on mirrors. You can can find them in the search and just follow fron whatever instance you use so there is no need to focus on a mirror instance.

You can use bird.makeup, but a lot of instances defederate from it because of their particular rules, for example because the use of it is nonconsensual to the person on twitter or because they’re against big media/corp on their feed.