If for someone the "old" way of snapping windows and tabs to the tab bar is one of the crucial functionalities (like for me), I've found a solution for this problem. It seems that Opera 95 stable release is the best option and the only problem is forcibly maintain auto-update disabled. I've researched an auto-update subject a bit and I see it may be a bit of a problem.
Here's the short tutorial how to solve this issue:

Download and install latest release of Opera 95 from here: https://ftp.opera.com/pub/opera/desktop/95.0.4635.84/win/ - remember to select file that ends with Setup.exe or Setup_x64.exe, not Autoupdate one. Go to installation location and remove all other versions' folders, leave only "95.0.4635.84" one. Go inside this folder and remove all "opera_autoupdate" files. If you can't do this,
3a. Open Task Manager, go to Users (for Win10, I don't remember for other systems), find "opera_autoupdate.exe" and end this process. Remove scheduled startup Opera process, you can do this e.g. with CCleaner -> Tools -> Startup -> find and remove Opera assistant process from the list. Edit the shortcut you're using to run the Opera by changing Target from launcher.exe to opera.exe (I'm not sure if it has any effect, it's just to prevent launcher from running anything else) and add "--disable-update" in the end.
5a. If you're running Opera from the taskbar, unpin your current shortcut and drag'n'drop the one prepared in point 5. to replace it. This is important not to run the old shortcut, as it won't have the update disabled and it will spoil the whole operation by updating to the newest version.

So far Opera didn't update itself and this solution seems to be working properly - tabs are snapping like a charm, O-Menu icon is always on proper position and never disappears, window and tab management is back to normal.