after installing or also the file TMSMQTTPkgDXE14.bpi says
the following content: /* 'TMSMQTTPkgDXE14' Package */
GROUP ( bplTMSMQTTPkgDXE14.dylib TMSMQTTPkgDXE14_nonshared.a )
Surely this is not correct, because the RAD C++ linker also reports [ilink32 error] Error: 'C:\USERS\USER1\APPDATA\LOCAL\TMSSOFTWARE\REGISTERED\TMS MQTT\MSMQTTPKGDXE14.BPI' contains an invalid OMF record, type 0x2f

Is this the trial or registered version?
To what platform are you trying to compile?

registered version on Windows 10 Rad Studio 11.3

Can you double check the Win32 & Win64 library & output paths, i.e. that you're not trying to link with a Win32 BPL compiling a Win64 app or vice versa.

In c:\Users\Public\Documents\Embarcadero\Studio\22.0\Dcp\ after the installation it says
I copy the TMSMQTTPkgDXE14.bpi from this folder to the folder c:\Users\User1\AppData\Local\tmssoftware\registered\TMS MQTT\ where the faulty file was before. Then it works.

Please check your Win32 and Win64 library path, it should point to the correct directories.

What is the right path?
How does the wrong content get into the file TMSMQTTPkgDXE14.bpi?
The linker obviously looks for the bpi in the directory where TMS MQTT was installed.

In c:\Users\Public\Documents\Embarcadero\Studio\22.0\Dcp should be the WIn32 compiled package files and in c:\Users\Public\Documents\Embarcadero\Studio\22.0\Dcp\Win64 the Win64 compiled package files and your IDE paths should be configured to point to these paths for Win32 and Win64 respectively.