Refused to enter singapore

Trying to extend your stay by doing a visa run was NOT a good idea!
It does not work that way in Singapore. Instead, you should have contacted ICA instead and applied for an SVP extension.
(Applying for jobs, on the other hand, is allowed and did not cause your problem - it's just that they suspect you of working illegally!)

Now you CANNOT just go back to Singapore. You would be denied at the border again.
You need to first clear up the matter with ICA. You have to convince them that you DID NOT and HAD NO INTENTIONS TO work illegally. Wanting to attend an interview will not help in this respect - so cancel that appointment.
If you do not manage to clear this up, you will also not get a work pass and cannot take any job in Singapore.

You have interview schedules?

Is it possible that you ask them to interview you via video, so they can process the Pass for you (after you submit all scanned certified documents online to the company-superiors-HRD)?  Thats more feasible and applicable for your case I believe?

So when you come Singapore, you will be holding to your IPA letter from the Ministry of Manpower applied by your company-sponsor, and you will enter smoothly.

All the best!

By now I do not know what has happened with your situation...though. Just a thought. Thanks!