Good day! 
Itās a very known issue in Windows. 
Failed to find the game please launch it. Report this if the issue persists
tl;dr i dont think youre getting a tl;dr with this oneā¦
In BeamMPās case, on windows, code 3 and 4 all mean userfolder (beamng) and/or user profile folder (%USERPROFILE%) path registry entry read failure, on linux though, it means that somethingās wrong with your pfx (look around on this forum if youāre looking for beammp installation guide for linux. anyway its still just as annoying as the windows registry problem here. in short, donāt complicate things for yourself by jumping from one proton version to another, stick to 7 or 8 for now, though you COULD play natively too! if you still wanna play through proton then you gotta delete that pfx/284160 and try again lol). And no, despite what the mods or devs say it has NOTHING to do with pirated copies or whatever, they work just fine, the problem lies somewhere else, so, anyway, weāre gonna be working with the registry and itās a bit scary, buckle up if you wanna play BeamMP any time soon (until you reinstall Windows FROM SCRATCH off a fresh .iso, of course, because this is a matter of user shell folders, which are left untouched if you decide to āreinstallā it using Microsoftās recovery tools, which always were a joke), and listen close and listen carefully.
When youāre installing Windows you are required to set up a user name, if you type something that isnāt ANSI/ASCII, so Cyrillic, Japanese, Chinese, diacritics such as Ƨ, Ć£, Ć”, ĆØ, Ć¢, Ć¼, etc., basically anything that isnt strictly latin characters, you are unknowingly breaking many things in your system, namely the registry - VERY MUCH the registry. However, if a program is properly coded (unlike BeamMP), it should work with unicode. Hereās a fun read: Mojibake! Itās definitely not something that your system sees trying to read your corrupted username! Encoding and localisation are not related to this topic (I guess), but they also play an important role in file names. So, registry is something that people in the know absolutely despise. Linux and MacOS donāt have them and for a good reason! Itās just the old boomer Windows with its outdated legacy garbage āfeaturesā. To be completely honest with you, even the most nerdiest geekiest Windows āpower usersā donāt understand why such a thing still exists.
Anyway, where was I? Ah, yes. When you change your Windows username, be it during migrating your system from HDD to SSD (never copy system files, always reinstall windows!), upgrading from Win7 to Win10/11 or maybe you just simply renamed your user folder because you didnāt like your older nameā¦! Thatās all really great! NOT!!! I have some very bad news for youā¦ All of the above does not work on Windows, my deepest condolences, another victim by Microsoftā¦ No, it just doesnāt! I was there in your exact situation! And itās not your fault, never! Itās just that Microsoft are evil, always were, in very evil and really greedy and corrupt way. Sorry, I just really wanted to mention HOW DIGUSTING MICROSOFT IS! No, really, Windows is NOTORIOUS for being a TERRIBLE home use operating system. But what can we all do when itās the only piece of garbage that still worksā¦ Itās like a SUV that everyone drives, but is really annoying to drive yourself.
Look at these down below. Itās not the same error, but they stem from the same thing. It canāt find the path to your AppData because Microsoft happened.
Okay, letās get serious. A lot of words. Solution is next. If these characters (< > : " / \ | ? *) corrupt a folder, then what some unicode characters would do? Well, the program will fail to install because the user path cannot be found due to characters it cannot read. Although BeamMPās installer installs successfully, BeamMP launcher itself doesnāt work because it doesnāt support unicode. What is the solution? Well, we can sit and wait for maybe another 10 years before unicode support will be added by the BeamMP dev teamā¦ or we could fix your shell folders RIGHT NOW! So, since the BeamMP launcher reads directly from the AppData and Local AppData in HKEY_CURRENT_USER\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\Shell Folders, one would think it is sufficient just to rename it just like so: C:\Users\%USERNAME%. No, renaming a user folder does not automatically rename the user profile path in the registry. Besides, you wouldāve probably made a mess with symlinks and security identifiers. So, then one could change the entry in the registry themselves? Correct, one solution is to open run via Win+R, type regedit, create a backup, go to HKEY_CURRENT_USER\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\Shell Folders and edit AppData key with %USERPROFILE%\AppData\Roaming and then Local AppData key with %USERPROFILE%\AppData\Local and then preferrably everything else which uses the older (corrupted) user profile path. Remember to restart! Now, the %USERPROFILE% is an environment variable, so are %LOCALAPPDATA%, %APPDATA%, %SystemDrive%, %ProgramFiles(x86)% and %USERNAME%, these contain critical system resource locations such as special folders (they are built different), if one of these is reading non-existent paths, oi oi oi oi, weāve got ourselves a useless system unless you reinstall it again, that isā¦ Anyway, if you were to type these variables into run, it will open its assigned directory. Your error code 4? Check before and after the changes you made to the registry to see exactly where your system thought the paths were leading to. You might have used these ā%appdata%ā hacker phrases yourself if you were frequently installling mods (for minecraft).
BUT! If your %USERPROFILE% itself is corrupted, then you could try editing AppData and Local AppData paths with your NEW user folder name MANUALLY. For example, AppData would be C:\Users\Username\AppData\Roaming. This is the worst case scenario and is the deciding point of no return - your computer is, to put it lightly, Fād, so consider getting an empty flash drive ready and start downloading a fresh Win10.isoā¦ and DO NOT use any recovery tools by Microsoft, they leave your user shells untouched, problems WILL PERSIST!
BUT WAIT! If you are already contemplating reinstalling your OS or you are a very lazy person, or just simply not keen on editing the registry at all, there is a second, registry-less solution that you might prefer more which might even work! Create a new offline local administrator account! You probably know how to do it, but hereās a link anyway! This is not perfect, because IF one were to have a domain account or an online microsoft account with a linked first and last name with special characters in it, they would either A) have to change their online name B) not have the option at all, becauseā¦ Microsoft? Thereās many editions of Windows that can and cannot do some things. In enterprise (I donāt know what Iām talking about), global address lists and email headers are pretty important, so by changing anything - even one letter, that person might get into trouble (pft not that i care about corporations anyway). So! Weāre still gonna have a problem, besides we had to create a new user folder. Nevertheless, MAKE SURE your new user name does not have any special characters in it, everything should be ANSI/ASCII only. Then copy everything from your old user folder to your newly created one and - BOOM! - no registry needed. And like that, youāre sorted.
USUALLY nowadays software is written with this problem in mind. By āthis problemā I, of course, mean Microsoft and Windows, duh. It just doesnāt happen on Unix thoughā¦ But itās still hard to get it right. Even though BeamMP is an average student project, you canāt really blame them for being not able to handle unicode file names. Even BeamNG devs, a bit more experienced, but not as much as to fix all the 1 string bugs that linger for over 10 years without complaining about āfutureless approachesā, make mistakes. Stuff like input identifiers with unicode or even key input themselves if you are in the non-english locale. Oh, you know what Iām talking about, games that ignore all input until you change your language layout. Sometimes you even have to restart to apply even the littlest changesā¦ Itās THAT sensitive. So is the path to your BeamMP mod.
Moral of the story? Microsoft - bad, unicode in usernames - bad, make a new local account - good. Cool! 
Sorry, what am I even talking about? Iāve solved your problemā¦ I should go nowā¦ 
tl;dr your shell folders keys OR %userfolder% variable are corrupted, see registry