Changing employers while OPT STEM Extension is still under process and 1 year OPT is expiring or already expired

First time poster here, so please excuse any mistakes I make. I have landed in a tricky situation regarding my status and would appreciate any help or advice.
I graduated from my masters course on May 2020, I had received my 1 year OPT at that time with the expiry date of 30th June 2021. I worked as a volunteer assistant for a professor from my uni for about 6 months and then I finally got a full time job in January 2021.

I worked hard at this job for the past 5,6 months and then suddenly on 23rd June 2021, last week they told me that they no longer wish to continue my employment (why they did this is another can of worms I'm not gonna go into in this post). Now I had already sent my STEM OPT Extension application through this company which was received by USCIS on 5th May 2021 and which is still under process. I told them that my current OPT expires in a few days and that I am afraid that losing this job at this point might cause problems for my STEM extension. So they decided that they are going to help me by marking my last date of work after I receive my STEM Extension.

In the mean time I gave a interview for a consultancy and cleared it, I have received a offer letter from this consultancy on 29th June 2021, yesterday and the start date is mentioned as 6th July 2021. Now I know that the rules require you to update any changes in your employer within 10 days.

So I am confused what I need to do. Should I accept the offer letter from the new company and simply inform my university about my job change, even though my current OPT has expired on 30th June 2021 and my STEM OPT has still not finished processing. Should I speak to my my current and next employer and set things up such that the end date of my current job and the start date of my next job is only set after I get my STEM extension approved.

I just want to make sure that my current STEM extension does not get rejected and I maintain my F-1 status so that I don't get deported or end up having issues during my H-1B application in the future.

Any help is appreciated thank you.