iPhone 11 CPU is burned out, can't be charged, the battery is displayed at 1%, and it will automatically shut down after 2-3 minutes of power-on.

The phone can't be repaired if the CPU is toast. In terms of data recovery, you've been backing up your iPhone right? If yes, when you buy a new iPhone, you can set it up from the backup of your iPhone. If you haven't been backing up, your data is gone.

I went to the mobile phone store to replace the battery and power supply chip first.....

Was this an Apple authorized shop? If yes, you will find them listed in this roster of authorized service shops in your area.

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but it did not work

The phone should not have been returned to you until it was working correctly. What did the shop say about this?

So is there any way to solve this problem?

Well, if you took the phone to a non-authorized shop, an Apple authorized shop won't touch the phone now. We can't say whether an unauthorized shop can actually repair the phone, since they won't have access to genuine Apple parts.

Or is there any way to copy out all the data?

Not until the phone is working correctly again, if you are asking if the phone can be backed up. You do have other previous backups, correct?