@WhiteNoise
I found the source of the problem - it is Consistent attachments and links plugin. After it updates information of attached files in cache - it starts deleting these files on the server.
That’s what I did. Built everything again from scratch and completely synced ( upload) with the server. Once it synced, pressed the sync pause button. Then, immediately ran this plugin. After he updated information on all the attached files in the cache - I decided to check that will sync and what is not sync - I took off from pause and sync immediately began mass delete all pictures (many hundreds) from the server.
Console log and synchronization log I copied and saved separately - all files, for which the plugin updated the information in the cache, were deleted.