Ica problem

If I understand your posting correctly, you had (and used) two passports with different personal details at the same time? If so, that is of course a major problem for any buerocrat - and honestly I cannot imagine any possible constellation where this is legal.
But if you have written proof, from the Indonesian authorities, that this was o.k. and you were in your right to do so, then send that to ICA with a letter explaining the situation again in your own words. (The contact details are on their webpage.)
If not, you will probably be banned forever for using fake documents.

This was common in times of old when agents knew which immigration officers to pay for a dodgy passport.
Most were workers that had been nabbed for working illegally and wanted to go back to work again, or underage workers trying to earn a living.
The new electronic KTP and KPK activity has all but put a stop to that now, but there is still the possibility of someone trying it on.
That explains how the illegal fake passports were obtained, and possibly excuses the OP assuming she was only there to try to earn a living and all other paperwork was correct, but Sing's immigration people might very well take a dim view of it and make life hard work for her.
After all, they can pick and choose who enters for what, so what incentive to they have to allow a known illegal to return?

First and foremost, please avoid sending private messages to us. I’m getting lots of messages for seeking help.

Sending private message is not the correct approach as we want this forum should give benefits to all expats and that would happen only when we discuss and share information publicly.

Coming back to your query, send your details to the officer for seeking his/her confirmation that you can visit Singapore. Below link, I had shared multiple times for reference:
https://www.ica.gov.sg/technical

Good luck