I recently copied about 200GB of my Win11 audio media files, nearly all FLACs, directly to a microSDXC card using Beyond Compare 5 (BC5). For folders and files the Modification and Creation Dates were preserved, as reported by Windows Explorer. I then inserted that card into a Samsung Galaxy S9 phone (I realize this is not an option for the OP, but bear with me here...). All Modification and Creation Dates remain preserved for the card in the phone.
If I now copy files from Win11 directly to the card in the phone, the dates and times on the phone for the copied files are changed to the date and time of the file copy operation. There seems to be no satisfactory way around this - it is a fundamental restriction of Android's MTP communication protocol, as implemented by Samsung, when copying to the phone over a USB connection (widely reported elsewhere). AFAIK, the only way to preserve audio file dates in this scenario is to use file tags which are guaranteed independent of the OS date and time stamps. To check sync, I plan to work around this limitation by using BC5 to do file comparisons of Windows v.s. phone based on last changed date & time, and then, when necessary, follow up with binary file compares for those files with recent unmatched date & time stamps. Maybe every few months I'll remove the card from the phone and start afresh to get correct date & time stamps. Cumbersome, but seems feasible.
Next I tried to make sense of MC's sync functionality - rather difficult. As a simple test, I highlighted some tracks, then RMB > Send to > Drives & Devices > ...Galaxy S9 card. That resulted in MC creating a new Music folder on the card with copies of the tracks in it. But none of those copied files had any date stamp at all in Windows Explorer, BC5, or Windows File Properties! Nada! Also, the Windows File Properties was reduced to contain almost no information for these files.
So my conclusion right now is just forget about MC direct Copy and Sync functionality with regard to phone, mainly because neither Windows Explorer nor BC5 show any date information for files copied by MC.
7/29/2024 Minor edits for clarity.
Win11 Pro 64-bit | MC 32.0.58 | Samsung Galaxy S9 Phone with Android version 10 | Samsung 256GB ProUltimate microSDXC Card.