Have solved the problem. I have both the DSL and LTE connection active on my Telekom router, the Speedport-Pro. I have now switched off the LTE and it works.
Hope I could help someone.
To all others, thank you for your help.

Have solved the problem. I have both the DSL and LTE connection active on my Telekom router, the Speedport-Pro. I have now switched off the LTE and it works.
Hope I could help someone.
To all others, thank you for your help.

@magge Hab dich eben angeschrieben.

@sheikah know me unfortunately not so well, how can I fix the problem? or how to find the culprit? I can log in via the browser, so on the website.
Only the program itself has problems.
Via cell phone I could log in directly, without problems.
Shortly confirmed via browser and the launcher has worked.

@magge how exactly do i do that?

@sheikah This comes in response to the link:

hydra.faforever.com

,,{"error": "Error 404 - The requested route does not exist. Make sure you are using the correct path, domain and port."}"

Thanks for your help

@magge I was able to log in briefly last night around 11pm, with the launcher building very slowly.
Today it was again not possible.
I myself do not use VPN, tested the link ,,https://hydra.faforever.com/oauth2/token" with Edge, Firefox and Opera (Opera with built-in VPN). But I always got the same message: "Method Not Allowed".

Edit:
Are there special ports for the launcher?
I just tried it with my phone as a hotspot, it worked directly.
I have a router from Telekom. Possibly certain ports are closed.

Thanks for the help.

Can't log in, as soon as I log in via the browser and close the window, FAF loads some more, but then I get the message:
Uh oh
Error during login
Have already reinstalled the program several times, turned off anti-virus, etc.
The version is: v2022.4.1

Thanks for your help.

Edit:
Client Version: 2022.4.1
org.springframework.web.reactive.function.client.WebClientRequestException: handshake timed out after 10000ms; nested exception is io.netty.handler.ssl.SslHandshakeTimeoutException: handshake timed out after 10000ms
at org.springframework.web.reactive.function.client.ExchangeFunctions$DefaultExchangeFunction.lambda$wrapException$9(ExchangeFunctions.java:141)
Suppressed: The stacktrace has been enhanced by Reactor, refer to additional information below:
Error has been observed at the following site(s):
*__checkpoint ⇢ Request to POST https://hydra.faforever.com/oauth2/token [DefaultWebClient]
Original Stack Trace:
at org.springframework.web.reactive.function.client.ExchangeFunctions$DefaultExchangeFunction.lambda$wrapException$9(ExchangeFunctions.java:141)
at reactor.core.publisher.MonoErrorSupplied.subscribe(MonoErrorSupplied.java:55)
at reactor.core.publisher.Mono.subscribe(Mono.java:4400)
at reactor.core.publisher.FluxOnErrorResume$ResumeSubscriber.onError(FluxOnErrorResume.java:103)
at reactor.core.publisher.FluxPeek$PeekSubscriber.onError(FluxPeek.java:222)
at reactor.core.publisher.FluxPeek$PeekSubscriber.onError(FluxPeek.java:222)
at reactor.core.publisher.FluxPeek$PeekSubscriber.onError(FluxPeek.java:222)
at reactor.core.publisher.MonoNext$NextSubscriber.onError(MonoNext.java:93)
at reactor.core.publisher.MonoFlatMapMany$FlatMapManyMain.onError(MonoFlatMapMany.java:204)
at reactor.core.publisher.SerializedSubscriber.onError(SerializedSubscriber.java:124)
at reactor.core.publisher.FluxRetryWhen$RetryWhenMainSubscriber.whenError(FluxRetryWhen.java:225)
at reactor.core.publisher.FluxRetryWhen$RetryWhenOtherSubscriber.onError(FluxRetryWhen.java:274)
at reactor.core.publisher.FluxConcatMap$ConcatMapImmediate.drain(FluxConcatMap.java:415)
at reactor.core.publisher.FluxConcatMap$ConcatMapImmediate.onNext(FluxConcatMap.java:251)
at reactor.core.publisher.EmitterProcessor.drain(EmitterProcessor.java:491)
at reactor.core.publisher.EmitterProcessor.tryEmitNext(EmitterProcessor.java:299)
at reactor.core.publisher.SinkManySerialized.tryEmitNext(SinkManySerialized.java:100)
at reactor.core.publisher.InternalManySink.emitNext(InternalManySink.java:27)
at reactor.core.publisher.FluxRetryWhen$RetryWhenMainSubscriber.onError(FluxRetryWhen.java:190)
at reactor.core.publisher.MonoCreate$DefaultMonoSink.error(MonoCreate.java:201)
at reactor.netty.http.client.HttpClientConnect$MonoHttpConnect$ClientTransportSubscriber.onError(HttpClientConnect.java:307)
at reactor.core.publisher.MonoCreate$DefaultMonoSink.error(MonoCreate.java:201)
at reactor.netty.resources.NewConnectionProvider$NewConnectionObserver.onUncaughtException(NewConnectionProvider.java:198)
at reactor.netty.channel.ChannelOperationsHandler.exceptionCaught(ChannelOperationsHandler.java:129)
at io.netty.channel.AbstractChannelHandlerContext.invokeExceptionCaught(AbstractChannelHandlerContext.java:302)
at io.netty.channel.AbstractChannelHandlerContext.invokeExceptionCaught(AbstractChannelHandlerContext.java:281)
at io.netty.channel.AbstractChannelHandlerContext.fireExceptionCaught(AbstractChannelHandlerContext.java:273)
at io.netty.channel.CombinedChannelDuplexHandler$DelegatingChannelHandlerContext.fireExceptionCaught(CombinedChannelDuplexHandler.java:424)
at io.netty.channel.ChannelHandlerAdapter.exceptionCaught(ChannelHandlerAdapter.java:92)
at io.netty.channel.CombinedChannelDuplexHandler$1.fireExceptionCaught(CombinedChannelDuplexHandler.java:145)
at io.netty.channel.ChannelInboundHandlerAdapter.exceptionCaught(ChannelInboundHandlerAdapter.java:143)
at io.netty.channel.CombinedChannelDuplexHandler.exceptionCaught(CombinedChannelDuplexHandler.java:231)
at io.netty.channel.AbstractChannelHandlerContext.invokeExceptionCaught(AbstractChannelHandlerContext.java:302)
at io.netty.channel.AbstractChannelHandlerContext.invokeExceptionCaught(AbstractChannelHandlerContext.java:281)
at io.netty.channel.AbstractChannelHandlerContext.fireExceptionCaught(AbstractChannelHandlerContext.java:273)
at reactor.netty.tcp.SslProvider$SslReadHandler.userEventTriggered(SslProvider.java:804)
at io.netty.channel.AbstractChannelHandlerContext.invokeUserEventTriggered(AbstractChannelHandlerContext.java:346)
at io.netty.channel.AbstractChannelHandlerContext.invokeUserEventTriggered(AbstractChannelHandlerContext.java:332)
at io.netty.channel.AbstractChannelHandlerContext.fireUserEventTriggered(AbstractChannelHandlerContext.java:324)
at io.netty.handler.ssl.SslUtils.handleHandshakeFailure(SslUtils.java:443)
at io.netty.handler.ssl.SslHandler$7.run(SslHandler.java:2117)
at io.netty.util.concurrent.PromiseTask.runTask(PromiseTask.java:98)
at io.netty.util.concurrent.ScheduledFutureTask.run(ScheduledFutureTask.java:170)
at io.netty.util.concurrent.AbstractEventExecutor.safeExecute(AbstractEventExecutor.java:164)
at io.netty.util.concurrent.SingleThreadEventExecutor.runAllTasks(SingleThreadEventExecutor.java:469)
at io.netty.channel.nio.NioEventLoop.run(NioEventLoop.java:503)
at io.netty.util.concurrent.SingleThreadEventExecutor$4.run(SingleThreadEventExecutor.java:986)
at io.netty.util.internal.ThreadExecutorMap$2.run(ThreadExecutorMap.java:74)
at io.netty.util.concurrent.FastThreadLocalRunnable.run(FastThreadLocalRunnable.java:30)
at java.base/java.lang.Thread.run(Thread.java:833)
Caused by: io.netty.handler.ssl.SslHandshakeTimeoutException: handshake timed out after 10000ms
at io.netty.handler.ssl.SslHandler$7.run(SslHandler.java:2113)
at io.netty.util.concurrent.PromiseTask.runTask(PromiseTask.java:98)
at io.netty.util.concurrent.ScheduledFutureTask.run(ScheduledFutureTask.java:170)
at io.netty.util.concurrent.AbstractEventExecutor.safeExecute(AbstractEventExecutor.java:164)
at io.netty.util.concurrent.SingleThreadEventExecutor.runAllTasks(SingleThreadEventExecutor.java:469)
at io.netty.channel.nio.NioEventLoop.run(NioEventLoop.java:503)
at io.netty.util.concurrent.SingleThreadEventExecutor$4.run(SingleThreadEventExecutor.java:986)
at io.netty.util.internal.ThreadExecutorMap$2.run(ThreadExecutorMap.java:74)
at io.netty.util.concurrent.FastThreadLocalRunnable.run(FastThreadLocalRunnable.java:30)
at java.base/java.lang.Thread.run(Thread.java:833)