As @Kender013 suggested, the AttinyCore works better than the core that is recommended in the official tutorial. With AttinyCore there are fewer problems with libraries.
I also made a video for it:
https://www.youtube.com/watch?v=AeqCEFF68QM

Some attiny88 sometimes have a bootloader problem, that's why these modules can't be programmed by USB. This problem is present if when you plug in your card or you press reset and the red led does not flash.

This problem is quite easy to solve, just install a special library and re-burn the bootloader.
I made a video to help people who have this problem:
https://youtu.be/KMaswFV8Xhs

I hope it can help too.

I posted another video, please watch this one first: https://youtu.be/54DCSPr-xIE
normally it should work like this (tested successfully on 3 pc)

If it helps, I made a video for it. I manage to program the attiny88 under Windows 10 well even with the error message (USB not recognized etc).
https://youtu.be/20ju2ghbdEs
Tell me if it works for you.

@Gatis @Ghibli_69 Yes I also had the exact same problem. But that doesn't prevent programming the board, I made a video for that: https://youtu.be/20ju2ghbdEs