Need Help with Flatpak, Repo seems incomplete, No matches found

I’m trying to install some Flatpak apps but it seems that they’re missing from the Repo.
I’ve tried it with my newly setup RaspberryPi4 (latest Raspbian Lite) as well as WSL-Deb12. I had the same problem for my WSL but it somehow works now.
So I’ve looked up the installed remotes and searched for lutris, wine, proton and bottles on both of my devices and copied the results here.

I’m now utterly confused on why that is and appreciate any help in advance.

I use the alias fs=‘flatpak search’
My Rasbperry Pi:

p@raspi-p:~ $ flatpak remotes
Name    Options
flathub system
p@raspi-p:~ $ fs lutris
No matches found
p@raspi-p:~ $ fs wine
Name                 Description                                             Application ID       Version Branch Remotes
Twine                Twine is an open-source tool for telling interactive, … org.twinery.Twine    2.7.1   stable flathub
Tellico              Collection Manager                                      org.kde.tellico      3.5.2   stable flathub
Minecraft Bedrock L… Download and play Minecraft Bedrock Edition on GNU/Lin… ….mrarm.mcpelauncher v0.12.0 stable flathub
p@raspi-p:~ $ fs proton
Name      Description                                                 Application ID              Version Branch Remotes
Proton V… Trusted and easy-to-use VPN app for Linux                   com.protonvpn.www           4.1.0   stable flathub
ludusavi  Back up your PC video game save data                        …github.mtkennerly.ludusavi 0.21.0  stable flathub
Ten Forw… Configure port forwarding on your gateway through the NAT-… fr.sgued.ten_forward        0.2.1   stable flathub
p@raspi-p:~ $ fs bottles
No matches found
p@raspi-p:~ $

My PC with WSL-Deb12

p@WSL:~$ flatpak remotes
Name    Options
flathub system
p@WSL:~$ fs lutris
Name          Description                             Application ID           Version        Branch       Remotes
Lutris        Video game preservation platform        net.lutris.Lutris        0.5.14         stable       flathub
p@WSL:~$ fs wine
Name          Description                                        Application ID         Version     Branch       Remotes
Wine          Run Windows applications on Linux, BSD, Solaris a… org.winehq.Wine        8.0.2       stable-23.08 flathub
Wine          Run Windows applications on Linux, BSD, Solaris a… org.winehq.Wine        8.0.2       stable-22.08 flathub
Wine          Run Windows applications on Linux, BSD, Solaris a… org.winehq.Wine        7.0         stable-21.08 flathub
Wine          Adds support to Fightcade for running emulators i… …htcade.Fightcade.Wine             stable       flathub
q4wine        Utility for Wine applications and prefixes manage… ….org.brezblock.q4wine 1.3.13      stable       flathub
WineZGUI      Wine GUI using Zenity                              ….fastrizwaan.WineZGUI 0.98.4      stable       flathub
PlayOnLinux 4 Graphical front-end for Wine                       …yonlinux.PlayOnLinux4 4.4         stable       flathub
Wineglass     A GUI for Wine                                     …hub.aggalex.Wineglass 1.1.2       stable       flathub
Phoenicis Pl… Install and run Windows software on Linux          …phoenicis.playonlinux 5.0-alpha-3 stable       flathub
Protontricks  A simple wrapper that does winetricks things for … …Matoking.protontricks 1.10.5      stable       flathub
Lutris        Video game preservation platform                   net.lutris.Lutris      0.5.14      stable       flathub
Bottles       Run Windows Software                               com.usebottles.bottles 51.9        stable       flathub
Mono          .NET Framework implementation for Wine based on M… org.winehq.Wine.mono               stable-23.08 flathub
Mono          .NET Framework implementation for Wine based on M… org.winehq.Wine.mono               stable-22.08 flathub
Mono          .NET Framework implementation for Wine based on M… org.winehq.Wine.mono               stable-21.08 flathub
Gecko         Web engine for Wine based on Mozilla Gecko         org.winehq.Wine.gecko              stable-23.08 flathub
Gecko         Web engine for Wine based on Mozilla Gecko         org.winehq.Wine.gecko              stable-22.08 flathub
Gecko         Web engine for Wine based on Mozilla Gecko         org.winehq.Wine.gecko              stable-21.08 flathub
DXVK          Vulkan-based implementation of D3D9, D3D10 and D3… …winehq.Wine.DLLs.dxvk 2.3         stable-23.08 flathub
DXVK          Vulkan-based implementation of D3D9, D3D10 and D3… …winehq.Wine.DLLs.dxvk 2.3         stable-22.08 flathub
DXVK          Vulkan-based implementation of D3D9, D3D10 and D3… …winehq.Wine.DLLs.dxvk 1.10.3      stable-21.08 flathub
ProtonUp-Qt   Install Wine- and Proton-based compatibility tools net.davidotek.pupgui2  2.8.2       stable       flathub
ProtonPlus    A simple Wine and Proton-based compatiblity tools… com.vysp3r.ProtonPlus  0.4.9       stable       flathub
Twine         Twine is an open-source tool for telling interact… org.twinery.Twine      2.7.1       stable       flathub
HyperPlay     Web3 game launcher from the future. Carry your wa… …z.hyperplay.HyperPlay v0.10.0     stable       flathub
Tellico       Collection Manager                                 org.kde.tellico        3.5.2       stable       flathub
Minecraft Be… Download and play Minecraft Bedrock Edition on GN… io.mrarm.mcpelauncher  v0.12.0     stable       flathub
XIVLauncher   Launcher & seamless Linux integration for Final F… dev.goats.xivlauncher  1.0.6       stable       flathub
Heroic Games… An Open Source Epic Games, GOG and Amazon Prime G… …roicgameslauncher.hgl v2.11.0     stable       flathub
XIVLauncherCN Launcher & seamless Linux integration for Final F… …tercorp.xivlaunchercn 1.0.6.2     stable       flathub
p@WSL:~$ fs proton
Name          Description                                      Application ID                    Version  Branch Remotes
Proton (comm… Latest Proton version built on the Flatpak Free… …e.Steam.CompatibilityTool.Proton 7.0-5    stable flathub
Proton-GE (c… Latest Proton-GE version built on the Flatpak F… …team.CompatibilityTool.Proton-GE 8.16-1   stable flathub
Proton VPN    Trusted and easy-to-use VPN app for Linux        com.protonvpn.www                 4.1.0    stable flathub
Proton Mail … Seamlessly encrypts and decrypts your mail as i… ch.protonmail.protonmail-bridge   3.7.1    stable flathub
thcrap-steam… A wrapper script for integrating the Touhou Com… …lity.thcrap_steam_proton_wrapper          stable flathub
Protontricks  A simple wrapper that does winetricks things fo… com.github.Matoking.protontricks  1.10.5   stable flathub
ludusavi      Back up your PC video game save data             com.github.mtkennerly.ludusavi    0.21.0   stable flathub
Celeste       Sync your cloud files                            com.hunterwittenborn.Celeste      0.8.1    stable flathub
ProtonUp-Qt   Install Wine- and Proton-based compatibility to… net.davidotek.pupgui2             2.8.2    stable flathub
ProtonMail I… Import emails to your secure ProtonMail inbox o… …ail.protonmail-import-export-app 1.3.3    stable flathub
ProtonPlus    A simple Wine and Proton-based compatiblity too… com.vysp3r.ProtonPlus             0.4.9    stable flathub
HyperPlay     Web3 game launcher from the future. Carry your … xyz.hyperplay.HyperPlay           v0.10.0  stable flathub
Steam         Launcher for the Steam software distribution se… com.valvesoftware.Steam           1.0.0.78 stable flathub
Heroic Games… An Open Source Epic Games, GOG and Amazon Prime… com.heroicgameslauncher.hgl       v2.11.0  stable flathub
ElectronMail  Unofficial desktop client for ProtonMail         com.github.vladimiry.ElectronMail 5.2.2    stable flathub
Ten Forward   Configure port forwarding on your gateway throu… fr.sgued.ten_forward              0.2.1    stable flathub
p@WSL:~$ fs bottles
Name           Description                Application ID               Version       Branch       Remotes
Bottles        Run Windows Software       com.usebottles.bottles       51.9          stable       flathub
p@WSL:~$

Not every package is available for aarch64.

The one you list are likely to NEVER be as they are meant to emulate legacy PC, aka Windows.

So, do I understand you correctly? Flathub does a hardware (or at least an architecture) check and just hides results if the packages are incompatible.