Mid 2014 MacBook Pro 13" Big Sur Issues

My laptop has been so great to me with no problems EVER. I updated to Big Sur 11.2.3 and my MBP all of a sudden shut off. I let it sit for a period of time and was able to get it to turn on, on occasions. But when it did it would shut back off randomly and the cycle continues. The battery would also not be detected at times.I was able to get it to turn on just long enough to reinstall Mojave and Catalina. Whenever I did that it would act fine for a while but as usage went on the problems began to reoccur once again. I talked to apple support, they are not able to do anything for me and set me up with my closest apple store (3 HOURS AWAY) so I went. My laptop froze up the apple store's diagnostic software when they plugged it in. They then told me they would keep it to troubleshoot so I left. I received an email with the techs comments on a problem and solution. HOWEVER I notices he left very critical issues out, and only put that is was overheating and randomly restarting. I contacted Apple numerous more times pleading with Bothe store and support to revise the techs statement because to me, the battery suddenly not being detected, along with the MBP starting to act funny as time went on while using were the two things to me that I felt would point in the direction of what was wrong. I was worried they would just reload Mac OS on the laptop, see it worked fine at first, then close it and call it a day. I received a call on day two saying it was ready yo pick up. SO I made another call to the store and support pleading for them to take ample time to figure out what is wrong, and that I rather take as long as neccisary , than for me to pick it up and the problem continue. HOWEVER Apple assured me it was fixed and nothing is wrong I with it so not to worry. SO I take off work and make the THREE HOUR drive to the apple store . The person brings my MBP out ANDDDDDDD...... it did not turn on. At this point the "genius's" were running around like chicken with their heads cut off. And proceeded to tell me there is nothing else they could do. I did some research before I even brought it in and 2013-2014 MBP 13" are having blacked out screens and the 2016-2017 MPB 13" is having battery problems in which Apple is replacing them free of charge. To me my issue seems to be these two things Apple has already addressed. However Apple is trying to say my MBP is "Vintage" and there is nothing they could do because it is hard to find part. This I don't buy considering the "genius" tried getting me to pay $300+ for a battery replacement and $300+ for the logic board. He gave me both prices because THEY DID NOT HAVE A CLUE WHAT IS WRONG WITH IT. But wait!? I thought it's vintage and you didn't have spare parts!? This is the worse experience I have ever had with Apple. In my opinion if Apple is confident enough to release an operating system which SUPPORTS my system, then the should SUPPORT the problems that it causes if they are publicly addressing there is a problem. Like a car recall. It doesn't matter the age. I do not care if it is so called "Vintage" it was working 100% PERFECT before the Big Sur Update !!!!! It is absolutely pathetic I spent 6 Hours today round trip to get the laptop they said was fixed when I all but begged for them to spend time on it because it will seem find at first. Has anyone else heard or have had these issues with their MBP? They were unable to tell me what was wrong with it and I intend on fixing and continue using it.