I've had this problem on Windows for years now, and I'm aiming to properly switch to Linux completely. And Opera looks, well, honestly very janky with flat windows and icons when compared to my desktop applications on Ubuntu MATE. I don't see how people tolerate it, honestly.

- Removal of the 32bit packages of chromium-based opera.
Since opera has dropped support for 32bit 2+years ago, please remove the 32bit packages from both the deb and the rpm repo.
Assuming that someone is advanced enough to first install opera's repo and then the browser from it, he can install opera's 32 bit version because the packages are still there! And this leads to more issues, like the one described here
https://forums.opera.com/topic/30291/www-lloydsbank-com-crashes-opera/

Codecs
It is built so as to the system's ffmpeg libraries, so its h264 (and other html5 codec) support is on par with the other browsers on the system.
In fact, I wanted to confirm it that much, that I asked the devs themselves on the project's page on github and they provided all the info.
I learned that the build flag
USE_SYSTEM_FFMPEG=true or false
that I had mentioned months ago no longer exists and now the same thing is done via 2 build flags
proprietary_codecs = true
and
ffmpeg_branding = "Chrome"
I checked them on chromium's build options on debian and arch and they are the same.

Search engines
Although there is no way to select the search engine when you right click on some highlighted text, because it defaults to google (or the one you select as default in options), you can delete the search engines you do not use.

Keeping up with chromium releases
I have to admit that its devs are doing a great work on that. There is a new release every time a new chromium release comes out from upstream.
Not even the chromium maintainers from my distro are that fast!
And for that reason, their releases are not tied to ubuntu's releases

Csd
Although the browser does come with its own csd, it can be disabled through its options menu.

These are my findings so far. There are also some other, less important (to me at least), e.g. the compatibility with extensions from the chrome store.
I won't be leaving opera anytime soon, but I think that if the devs of a lesser known browser can do all that, I am sure that the opera ones can too.

- Removal of opera and opera-next from the deb repo
They both are on v12.16, the last one using presto as the rendering engine, and they must have been there since 2014 or so.
Today, they are not even installable, due to the prehistoric dependencies they want

$ sudo apt-get install opera
Reading package lists... Done
Building dependency tree       
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
 opera : Depends: libgstreamer-plugins-base0.10-0 (>= 0.10.16) but it is not installable
         Depends: libgstreamer0.10-0 (>= 0.10.15) but it is not installable
         Depends: gstreamer0.10-plugins-good but it is not installable
E: Unable to correct problems, you have held broken packages.

$ sudo apt-get install opera-next 
Reading package lists... Done
Building dependency tree       
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
 opera-next : Depends: libgstreamer-plugins-base0.10-0 (>= 0.10.16) but it is not installable
              Depends: libgstreamer0.10-0 (>= 0.10.15) but it is not installable
              Depends: gstreamer0.10-plugins-good but it is not installable
E: Unable to correct problems, you have held broken packages.

So please remove them

Luckily, the yum (rpm) side of the repo contains only the latest packages.

- Ugly csd that can not be removed
https://forums.opera.com/topic/28146/opera-55-getting-rid-of-that-ugly-csd/

p.s. If there is any mod that knows the reason it was locked, please pm me.

And you are probably right about the delay due to reborn 3, but try explaining that to a simple user like the ones that started the 3 threads yesterday. All with a different subject/issue yet all pointing to the same problem.
For most of us, regular functionality is more important than a redesign.

Opera 58 is based on Chromium 71, Opera 59 would be based on 72 and 60 is based on 73, that's what I said.

https://help.opera.com/en/opera-version-history/

Opera 59 (chromium 72 based) is not in beta anymore, while opera 60 (chromium 73 based) is on both beta and developer channels. In fact, given the existing mess, I would not be suprised if opera stable skipped 59 completely and went straight to 60. That would be the best solution imho.

On top of that, let me make an example of how chromium's versioning works in relation to time, and compare it to how opera's versioning does.

• Today, chromium 73 is in stable, 74 is in beta and 75 is in dev. The day that 74 reaches stable, 75 will become beta and 76 will become dev. On the very same day, without any delay.
  The same happens in firefox too, but firefox is a different story, not related to ours.
• In opera though, things are different. I will use a different set of version numbers because today's is messed up with opera stable being on 58 and both beta and developer being at 60, Let's say opera stable is at 58, opera beta is at 59 and opera developer is at 60 today, so that the number "match".
  If opera 59 becomes stable tomorrow, opera beta will stay at 59 and developer will stay at 60 for some time When will they be updated? Sometime in the following days and not on the same day again, because there is no real schedule about it!

And that is what bugs me above when I say that 3 branches are too much for the devs to handle.

- Keeping up with chromium releases
As of today (March 22nd, 2019), opera stable is still based on chromium 71, which means it lags 2 major versions behind,
That delay became visible, again, yesterday that ubuntu upgraded chromium and chromium ffmpeg codecs to 73 and there are already THREE threads with the usual "vids are not playing today, but they did play yesterday" complaint. And all of them are from ubuntu (or ubuntu-based distro) users.
Its more than obvious that opera's 3 channels of development (stable, beta and developer) just can't keep up with chromium's 3 (stable, beta and dev). So why don't wou just drop one and keep stable and beta for instance, like you do on the for mobile opera and opera mini?
I hate to say it, but I assume you know which chromium based browser, and a good opera alternative (as considered by many people but not me) does that: vivaldi. (stable and snapshot versions).

- Stable releases tied to ubuntu's releases of chromium (?)
I am pretty sure the opera team is waiting for ubuntu to package the next version of chromium before releasing the next version in line for stable.
Of course this does not apply for the last 2 versions of chromium, because of the above reason.
So, although I can not recall the exact version or opera and chromium, I can recall at least one time that the slow pokes of ubuntu packaged chromium 3-4 WEEKS after its official release. And opera followed, relaasing the next version on stable channel a couple of days later. Needless to say that almost ALL distros had packaged chromium in the first 10 days or so.
Why should someone, regardless of distro, wait for ubuntu's maintainers in order to see an update for his/her main browser?

- Extensions bar out of nowhere
From time to time, the extension bar pops up on the side of opera for no reason. I have no extensions that use the side bar, only ublock origin, so why does it pop up?

I have had this issue a few times, recently also. The extensions sidebar just appears for no reason.

Oddly, only ublock origin appears in the extensions bar, which means it is "extetensions bar" capable. Upon clicking it, the usual logger of ublock comes up in the sidebar, so that's probably why.

(I fixed your typo, and hence deleted the comment about it.)