Do I have to format shared folder in Synology to make Time Machine possible?

FWIW, I have a Synology DS916+ and have been using it for Time Machine since 2018. I used the following Synology Support article to set it up:

• How do I back up files from my Mac to Synology NAS using Time Machine? - Synology KB

DSM, the Synology's operating system does not support creating APFS-formatted drives ... and, they would be totally unnecessary in this case. I just used the default bfrs formatting for each of the four drives in my NAS, and then, used that support article to configure a "share" for Time Machine.

Since macOS Sierra+ supports SMB3, make sure it is enabled in DSM > File Services > SMB/AFP/NFS > SMB > Advanced Settings > Maximum SMB protocol: SMB3 & Minimum SMB protocol: SMB2. You do not want to use AFP.

Any disk used for Time Machine must be properly formatted. As I understand it, Time Machine actually does that when setting it up. In the alternative you could do what I've always done. When I get a new external disk I first use Disk Utility to erase and reformat the disk. I never use any of the so-called maintenance software that comes with the disk. I've found that they can cause problems. Then it's just a matter of opening Time Machine and following its instructions. The process is not complex.

Tom, the two links you included in your post, are great to follow. You don't specifically need to format the shared directory (That is what it is on the NAS) that will appear on your friends mac as APFS. That is for direct connected hard drives. I didn't watch the video but in the research I've done be sure to set the share limit to 1.5X the size of the drive of the mac. Otherwise the Time Machine backup will eventually take up all the space on the NAS.

Hope this helps.

Paul