How to safely use Apple Diagnostics on a refurbished MacBook with migrated data?

When setting up a new Mac you can either migrate from an old system, or migrate from a Time Machine backup. Both are fine.

My concern is that you may not have any backups at all. If the data on your internal SSD is important (or any data on external data drives or in the cloud), then you need to make sure you have good backups of that data. The more important the data, the more backup copies you should have. FYI, cloud file syncing services are not backups. There are a lot more new ways to permanently lose access to the data stored on the internal SSD of the recent Macs due to all of the hardware, software, and security changes.

Kernel Panics can be caused by hardware or software issues. Most software issues that cause Kernel Panics are from using anti-virus software, cleaning/optimizer apps, and third party security software.....none of which are needed on a Mac. These types of apps usually cause more problems than they solve because they interfere with the normal operation of macOS at a low level. If you have any of these types of apps installed, then uninstall them by following their developer's instructions.

For hardware issues, make sure to disconnect all external devices in case one of them is causing a problem. Beyond that, the only way to confirm a hardware issue is if the Apple Diagnostics report a problem or if the failure also occurs with a clean install of macOS which involves erasing the disk & reinstalling macOS and thoroughly testing before installing any third party software and before migrating or restoring from a backup.

You can post several of the Kernel Panic logs so we can review them. These Kernel Panic logs are located in "/Library/Logs/DiagnosticReports" with file names containing "kernel" and/or "panic". Post them here by using the "Additional Text" icon which looks like a piece of paper on the forum editing toolbar.

You can also run the third party app EtreCheck and post the complete report here so we can examine it for clues. Just know if any of those apps I previously listed are shown in the report, you will be instructed to fully uninstall them before you will receive any more assistance since they are too often the source of the problem.

How to use the Add Text Feature When Posting an EtreCheck Report - Apple Community

Apple Diagnostics does not change anything. It is just a diagnostic tool to report any problems.

Using Apple Diagnostics should not cause any issues with your data. But, and this is a big but, you're working with a flawed machine and therefore there is always a risk of dataloss or corruption. So your first step is to make a back up - or two - of the data on that machine. Then, protected by that, you can do whatever with some comfort from your back ups.

I see. That was hard to understand since your question was "How to safely use Apple Diagnostics on a refurbished MacBook with migrated data?", and you made no mention of Time Machine.

I think it best if someone else helps.