Emulator

can just quickly install a deb package when using Linux

This is making an assumption that a .deb package can be installed on any Linux distribution. This is not the case. A .deb package would only work for the distribution and distribution version it was made. For example, if a .deb was made for Debian 11, it is not going to work with Debian 10, and it is unlikely to work with Debian 12. And of course, a .deb made for Debian will probably not work on Ubuntu and vice versa. Debian, Ubuntu, and distributions based on them are the only ones that can install .deb packages in the first place (as they use the apt package manager), other distributions cannot use them.

A .deb is also really not intended for applications to distribute themselves, it is intended for the apt package manager (apt uses .deb files internally). Hence why it has such limitations, it is intended that you have a .deb package made for each Linux distribution and distribution version, which the package manager handles obtaining the correct version to install, and package repositories handle storing all these versions. Debian and Ubuntu also already provide fairly modern packages for Dolphin for their latest versions:
https://packages.debian.org/bookworm/dolphin-emu
https://packages.ubuntu.com/oracular/dolphin-emu

If your distribution and/or distribution version does not provide a package or it's too old for your taste, you can use Dolphin's provided flatpak or compile Dolphin yourself. Compiling Dolphin yourself also only has most of the time spent on the initial compilation, typically future compilations would be much quicker.

I think integrity of flatpaks on flathub isn't well-checked

The flatpaks on Dolphin's website are built by Dolphin themselves. The flatpak repository is managed by Dolphin themselves. The issue you linked simply does not apply for Dolphin's case due to this.

Thanks for explaining. I think a deb file would work for multiple version of Debian and it would also make things easier even if it didn't work on all distros, one could also add a .rpm package. If a newer version than the one in the Debian repos including backports is needed then a .deb file is the easiest and maybe best way, it's very quick to install. Much quicker and with less troubles than building from source. A hashsum of the .deb file would be somewhere.

If your distribution and/or distribution version does not provide a package or it's too old for your taste

On the Download page there is no mention of it being available in the distro repos, maybe that's offtopic here but I think it should also be recommended instead of just explaining how to install the flatpak.

I think a deb file would work for multiple version of Debian

In theory, this is technically possible. In practice, that only really applies for more basic applications with few dependencies (e.g. just some basic CLI app). Applications like Dolphin are complex with many dependencies. With how .debs work, the more dependencies you have, the most likely the .deb will not work on a future distro version. One immediate example would come with Dolphin normally having a dependency on libavcodec (and its friends), which constantly has ABI breaks, thus incrementing the ABI version, resulting in a different package name (so apt won't be able to find the package) and a different .so.XYZ name (so ld wouldn't be able to find the library when trying to launch Dolphin, thus Dolphin would fail to start at all if you were to half-install that Dolphin .deb). This is just one example anyways, with more dependencies come at a risk of running into this kind of issue (that LLVM dependency you mentioned is also an example of such).

one could also add a .rpm package

This proceeds to just have the same issue as before: this is just a package you normally expect out of a package manager repository, not the developer. It also then only covers distros which support such a package manager, and ones which happen to have the same exact dependency packages available with compatible versions (this is very easily not the case).

The Flatpak here is something nearly every single distro would end up supporting (read: Debian does not get special treatment), as the flatpak system can be seen as a semi-independent distro itself, along with the flatpak package having most of its dependencies bundled, thus not strictly bound to one distro nor another. They'll continue to work even like 10 years afterwards, unlike .debs/.rpms/whatever native package which have a time limit before they're completely useless.