Whilst I cannot provide direct help (yet). I have the same problem and it only affects one out of two of my rpi3B. I have opened tickets on raspberrypi.org and will try to continue figuring out the problem.
The problem is not the upgrade from jessie. I'm on buster since months and this problem was introduced with an update around May 15th for myself, according to kernel logs.
cat /var/log/kern.log | grep smsc95xx
May 15 07:32:19 raspberrypi kernel: [ 1.383694] usbcore: registered new interface driver smsc95xx
May 15 07:32:19 raspberrypi kernel: [ 4.244294] smsc95xx v1.0.6
May 15 07:32:19 raspberrypi kernel: [ 4.341748] smsc95xx 1-1.1:1.0 eth0: register 'smsc95xx' at usb-3f980000.usb-1.1, smsc95xx USB 2.0 Ethernet, b8:27:eb:af:f3:f4
May 15 07:32:20 raspberrypi kernel: [ 12.852984] smsc95xx 1-1.1:1.0 eth0: hardware isn't capable of remote wakeup
May 15 07:32:21 raspberrypi kernel: [ 14.416414] smsc95xx 1-1.1:1.0 eth0: link up, 100Mbps, full-duplex, lpa 0xC5E1
May 15 23:43:17 raspberrypi kernel: [ 1.406684] usbcore: registered new interface driver smsc95xx
May 15 23:43:17 raspberrypi kernel: [ 3.934275] smsc95xx v1.0.6
May 15 23:43:17 raspberrypi kernel: [ 4.031511] smsc95xx 1-1.1:1.0 eth0: register 'smsc95xx' at usb-3f980000.usb-1.1, smsc95xx USB 2.0 Ethernet, be:b8:2d:47:47:04
May 15 23:43:18 raspberrypi kernel: [ 12.379286] smsc95xx 1-1.1:1.0 eth0: hardware isn't capable of remote wakeup
May 15 23:43:19 raspberrypi kernel: [ 13.894849] smsc95xx 1-1.1:1.0 eth0: link up, 100Mbps, full-duplex, lpa 0xC5E1
b8:27:eb:af:f3:f4 Raspberry Pi Foundation
be:b8:2d:47:47:04 Vendor not Found
So you likely tried these already
https://raspberrypi.stackexchange.com/questions/68513/pi-using-a-random-mac-address-after-every-reboot-how-do-i-stop-this-behavior
and
https://www.raspberrypi.org/forums/viewtopic.php?t=33252
I will try to add links here once the admins approve my troubleshooting threads there.
May I ask, do you boot from USB or SD card? Meanwhile I give this a thumbs up, this problem needs to be brought to attention. It even persists for me when I return back to old official stock images of buster.
Edit:
The topic is live now https://www.raspberrypi.org/forums/viewtopic.php?f=28&t=274220