hi all. some urgent help needed.

I am working in SGH. 10+ years of experience as an AHP, graduating with a degree end 2022.
applied to a job under singhealth cluster, and got it.
however, because it is considered a lateral transfer, and i went into my current job as a dip grad, HR offered me based on my current JG. (JG11). which is even worse than a fresh grad (JG12). have gotten performance awards twice in my 5 years with my current company, and also had good PR grading.
expressed my discontent, but HR said there is nothing she can do about it, even after speaking to the managers.

taking it seems like a disservice to myself. but private sector wont be able to offer what my new place has in terms of benefits, clinical exposure. my field is vv niche. so i feel so stuck atm.

yesterday, wanted to accept the job already, and actually called HR ytd to ask one more question to verify before accepting it. however, when speaking to HR, HR said that the hiring managers may retract my offer as i expressed that i wanted better terms but they were limited by policies across the board. is this even allowed? what should i do now?