I think it's time to take a next step, 4K hi-dpi interfaces are everywhere. There have been previous requests in recent years.
Tixati icon in dock and Software app in fresh install of Debian stable with Gnome looks worse than others (most guidelines set target to at least 128×128):
https://files.catbox.moe/geal06.png
Ironically, even favicon.png for this site, which is 64×64, is bigger than bundled 48×48 one.
Note that you can provide an SVG file to handle arbitrary resolutions, and the vector icon that fits the template should be simple enough to create even for amateurs. I could try to make a copy of the old one myself, but it would be a bit impolite to the author.
https://specifications.freedesktop.org/icon-theme/latest/#install_icons
https://developer.gnome.org/hig/guidelines/app-icons.html
You can also notice that the application screen is a bit empty. What's more important, after installation Tixati is not listed among installed applications in Gnome Software, and pressing About in the context menu for the dock icon produces the error instead of the program page. You need to use the list of applications in System Settings to uninstall Tixati, or open .deb file with Software once again to see the desired page with Open and Uninstall buttons.
This is due to the lack of AppStream metadata file, and automatic generation of a ghost one for tixati.desktop file.
https://www.freedesktop.org/software/appstream/docs/chap-Quickstart.html
https://blogs.gnome.org/tbernard/2021/09/07/ready-for-software-41/
https://blogs.gnome.org/uraeus/2022/06/10/how-to-get-your-application-to-show-up-in-gnome-software/
It's a very simple format that I quickly generated with their web tool and put where it belongs. The difference is clear:
https://files.catbox.moe/jr1lp9.png
There is a catch, though. Official documentation assumes that everyone uses unique IDs like
com.tixati.tixati, and validates that. Debian, on the other hand, in its backward-compatible glory, is fine with
name.desktop or even unique strings for packages. They also use more efficient format for local storage of all metadata from the official repository (after all, it is a first party software management tool in Gnome edition).
https://wiki.debian.org/AppStream/Guidelines
It seems that the solution people choose is using reverse domain ID for both metainfo and .desktop file name to satisfy both requirements.
https://salsa.debian.org/games-team/woof-doom/-/tree/master/data
Another crucial part is placing the old ID,
<provides>
<id>tixati.desktop</id>
</provides>
into a new metainfo file, as mentioned in
https://blogs.gnome.org/hughsie/2019/07/05/fun-with-the-odrs-part-2/
Supposedly, when you put that AppStream metadata into .deb or .rpm package, it will magically work for installation and uninstallation, and also for program properties page, and we even get the 10 five star reviews people have made transferred to a new ID.
Of course, that would require making a couple of up-to-date screenshots to put on the website.
Supposedly, when that metainfo file license is free/permissive (file itself, not the program it describes), it can also be included in global databases, though I don't know how it works for third party closed source packages.
P.S. I do not really endorse Gnome Software tool, in a typical Gnome fashion, they know what's better for their users:
https://discourse.gnome.org/t/gnome-software-the-app-store-has-cookie-like-user-tracking/29198/
However, it is what many Linux users are going to see, and there is no reason to make it look worse than it can be.