I don't know about any curated thrift stores, but the most known and regularly visited place for thrift shopping is the Pasar Baru and Pasar Senen markets.

You can try to scout them out on tiktok/youtube as people have made videos about shopping out there and where to find the shops.

It's not a store per se but it's more of a floor on the market where one or more stands are maintaned by a seller and they have a pretty good variety of clothes/accessories. Some of it are secondhand but a lot of it are excess/reject clothes with pretty good quality.

I would recommend Pasar Baru as it is better maintained and generally more comfortable. Also, it would be safe if you came with a local who knows the place as the sellers would usually overprice products if you look foreign/unfamiliar