Is there any way to report a complaint regarding a Genius Bar experience?

Apple won't see your post here, and there is no longer an electronic way to report issues with sales, service, or support.

Instead, see my response in this recent thread:

How do I file a complaint directly with A… - Apple Community

HaileyKoo wrote:

I used to work in retail too, so I understand how sales strategies work and how staff are trained to upsell.

That may be true of retailing in general, but Apple Store representatives do not earn sales commissions. It has been my experience that their primary objective is to listen to their customer's needs to help them make an informed purchase decision. They want happy customers.

Also I would not expect a properly trained Genius Bar associate to describe a logic board as "burnt" unless it suffered fire damage. Otherwise, it's imprecise at best. Components and systems can fail for a variety of reasons. Those reasons can be identified and explained but it's almost always uneconomical to do even that much. If someone were to tell me a logic board was "burnt" I would quickly lose confidence in anything else they had to say. I'd stop listening. I'd probably just walk away.

Component level repair became a lost art decades ago. If a logic board fails, it can be replaced, but considering most Macs have been single board computers since their inception the logic board comprises nearly all of its cost and complexity. If a Mac is new or nearly new, sure, replace it. If it's more than a few years old, replacing a failed logic board becomes economically unjustified.

Not having been party to that conversation, I believe that's what they were trying to tell you.

How can I let Apple know about this?

Others already answered that question but as a practical matter it's not productive to do so. Register your complaint and move on.

1. Buy a new computer.
2. Make sure you keep backups of your data so that you do not lose "precious memories" on the new computer.
3. Computers become unsupported, obsolete, or vintage over time and are not worth the cost of repair.

Obtaining service for your Apple product after an expired warranty - Apple Support

There may be more to the technical side of this than meets the eye.

In almost all cases, 'repairing' the logic board (that holds almost everything in the computer) involves replacing the logic board. Apple does not do field repairs of customer logic boards.

If your Mac was released after about 2015, the boot drive was likely soldered to that logic board. Since the boot drive is essentially a fixed part the logic board, replacing the logic board TRASHES your files.

Despite your emotional attachment to this computer, 'repairing' it may not accomplish restoring your fond memories in any way -- out may simply discard them permanently and forever.

¿EXACTLY what model-year, processor, and screen size is this computer?

HaileyKoo wrote:

After some thought, I decided to repair my old MacBook since it holds a lot of precious memories for me.

Do you mean that literally or figuratively? If you are concerned about the contents of its storage device (hard disk or flash memory — you didn't identify your model Mac so we can only guess — the MacBook has not been produced for many years, so it's by definition quite old) then it will influence your decision.

If you simply have an emotional investment in the Mac that can influence your decision as well. No one but you can put a value on either of those aspects.

If you have (or had) an attachment to that Mac's stored contents and failed to maintain backups it must not have had much value to begin with.