Well, you are in a pickle!
Sounds like the power management and/or Thunderbolt 3 controller chips have a problem. This will require someone with deeper skills to dig deeper locally.
As far as getting to your data I hope you have been good in backing up, if not you’ll need to go to someone who has the data recovery tool to gain access to your logic boards data.
Here’s more on the tool its self: This is Apple’s special tool to help customers recover data from the MacBook Pro’s non-removable SSD
Not all of the Apple Store have it and some independents managed to get their hands on them when some stores threw them away! Most just tell the customer its a lost cause and they loose there stuff as Apple will only replace the logic board not fix it.
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