Can files or data remain on a macbook factory reset?

If you erase the Mac correctly (erase the "Volume Group") and reinstall macOS then nothing of the previous installation remains.

However, if the Mac is being managed by an organization's MDM (business or school), then that Mac may call home and start to reinstall the previous configuration profiles provided by the MDM. The business or school must correctly remove the device from their MDM management prior to selling the Mac since there is no way anyone else can remove this MDM connection.

matyas_is_taken wrote:

And if I reset the mac in the standard way according to the predefined procedures?

Correct.

Following the instructions in Erase your Mac and reset it to factory settings - Apple Support results in the complete and irretrievable erasure of your data — for your model Mac, similar M series Macs, as well as certain older models mentioned in that Support document.

matyas_is_taken wrote:

...Can installing programs like homebrew leave files behind when resetting the macbook to factory settings. Can some programs get installed too deep into macOS that the mac doesn't delete them during a reset?

The user @neuroanatomist is technically correct. Rotational HDDs can retain a magnetic imprint of data unless zero'd out. Disk Utility can do that, though it is time consuming. Someone with a specialized app may be able to recover that data. SSDs are functionally different and don't retain data after being wiped.

However, as to your third question - can some programs get installed too deep...? - no. Apps and files don't get installed in places that are safe from erasure. When either type of drive is properly erased, everything gets removed. All of the directories and indexes that tell a computer where files are stored get deleted.

Depends on the Mac. Older Macs with a spinning magnetic hard disk needed to be overwritten with zeros (a time-consuming step) or data remained after the drive was ‘erased’. With an SSD, when you Erase All Content and Settings, it’s wiped clean.

If you are asking about the Mac shown in your profile information MacBook Pro (M3 Pro, 2023) then the answer to that question is no.