dpkg -L opera-stable | grep ffmpeg
/usr/lib/x86_64-linux-gnu/opera/libffmpeg.so
/usr/lib/x86_64-linux-gnu/opera/resources/ffmpeg_preload_config.json

I tried remove the /usr/lib/x86_64-linux-gnu/opera/lib_extra/libffmpeg.so and videos play fine now on my PC.

@gloewa Copying random version from random place is not a reproducible solution.

It isn't, but the Opera programmers responsible leave you no other choice.
Like Opera, Vivaldi uses Chromium as its basis, but Vivaldi uses a functioning libffmpeg.so. I mentioned above [1] where Vivaldi gets the libffmpeg.so from.
[1] https://forums.opera.com/post/392484

ABI info is completely masked at unified .so (extractable from source code) and major ver of avcodec could be bumped even major ver of Chromium is not bumped.

this is what helped me every time this happend

I solved the problem for now by copying libffmpeg.so from the Vivaldi directory to the Opera directory. Now everything is working as usual again.

previous versions of opera could play videos, current version

A libffmpeg.so only works with a specific major version of Chromium. So, any time Opera starts using a new major version of Chromium, you have to update to a new libffmpeg.so that's based on that new major version of Chromium.

Historically, Opera started using a new major version of Chromium every time Opera updated to a new major version itself. So, you had to find a new libffmpeg.so each time Opera updated to a new major version (102 to 103 for example). In addition, since Opera Beta was a major version ahead of Opera Stable and Opera Developer was 2 major versions ahead, you'd need a different libffmpeg.so for beta and a different one for developer.

However, for a while now, Opera has been been slower on updating to new major versions of Chromium, so a libffmpeg.so's compatibility has been lasting a bit longer. But, libffmpeg.so still needs to be updated eventually.

Now, for the Snap package of Opera and the Snap libffmpeg.so it uses, it has slots for multiple major versions of Opera, which can make it so you don't have to worry about compatibility most of the time and stuff just works. So, try the Snap version of Opera if you want. Also, some users that don't use the Snap package of Opera put a symlink to the snap libffmpeg.so in Opera's "lib_extra" folder and have had good luck.

For the Flatpak package of Opera, the maintainer tries to make sure all is good with a compatible libffmeg.so, but sometimes it can go wrong.

If you don't want to deal with any of that though, it's best to use a different browser.

@alexs Are you kidding me? the linked opera-posting is from 2018!

That doesn't change the statement regarding the license.

@gloewa said:

Till few days ago all was as it should. The last update broke the video-functionality.
If opera is not able to fix it, its time to change to another browser. As simple as that.

I don't disagree with you. For me, I had to fix the video functionality myself once again.

Read https://forums.opera.com/post/392484

If opera is not able to fix it, its time to change to another browser. As simple as that.

Or, most probably, Opera thinks that even offering a script like that may have legal consequences.

Now, it is mentioned here that Opera cannot make the library available for legal reasons.[1]
However, that does not mean that you are allowed to download it from a third-party source after installation in order to use it later. And that is exactly what the script does. An official statement from Opera would be more than helpful to explain why Opera users on Linux have to make the browser functional themselves, which is ridiculous.

[1] https://forums.opera.com/post/150324
[2] FFmpeg License and Legal Considerations

But... Vivaldi has a very clever Linux programmer (Ruarí Ødegaard, former Opera employee), which is why the Vivaldi browser installation package contains a script called update-ffmpeg [1]. This script searches for the Vivaldi version, downloads the appropriate libffmpeg.so version, and copies it to /var/opt/vivaldi/media-codecs-xx.x/libffmpeg.so
Videos then work without any problems in Vivaldi.

Why doesn't this work with Opera? Perhaps it's because Opera doesn't have any programmers working on Linux, after all, there are many problems that only exist on Linux-based systems: Videos don't work, the Opera browser ignores the language of the operating system (only English), the browser does not remember the last window position.

About the videos that don't work for me (Debian/sid, Opera One: 122.0.5643.17):
I installed Vivaldi Stable and copied their working libffmpeg.so from /var/opt/vivaldi/media-codecs-120726/libffmpeg.so to /usr/lib/x86_64-linux-gnu/opera/lib_extra/libffmpeg.so.
Alternatively, you can also use the current Snap version [2] of chromium-ffmpeg.

mkdir -p /usr/lib/x86_64-linux-gnu/opera/lib_extra
copy /var/opt/vivaldi/media-codecs-120726/libffmpeg.so /usr/lib/x86_64-linux-gnu/opera/lib_extra/libffmpeg.so

[1] https://pastebin.com/DYJZTkf1
[2] https://api.snapcraft.io/api/v1/snaps/download/XXzVIXswXKHqlUATPqGCj2w2l7BxosS8_82.snap