After installing TMS MQTT pakage and start Delphi Sydney again, Delphi reported not found TMSMQTTPkgDEDXE13.BPL and a lot of other related MQTT packages.
Using EAverything, I found that TMSMQTTDEDXE12.bpl was installed alongside any other with 12 as looked for.
Can you send the installer generated log file in your Windows Documents folder so we can inspect what exactly happened on your machine?
What would the log name be ??
Please search for TMSMQTT*.log
Sorry to say, but there is no tmsmqt*.log around 
You look in the correct Windows Documents folder of the Windows user account with which you executed the installer? There should be a log file.
Yes, I use Everything, but when searching for TMS*.log, the following name did pop up
TMS MQTT_1.2.0.3.log
TMS MQTT_1.2.0.3.log (1.93 MB)
The error we see in the log file is:
C:\Program Files (x86)\Embarcadero\Studio\21.0\Bin\CodeGear.Delphi.Targets(402,5): warning MSB6002: The command-line for the "DCC" task is too long. Command-lines longer than 32000 characters are likely to fail. Try reducing the length of the command-line by breaking down the call to "DCC" into multiple calls with fewer parameters per call. [C:\Users\achristo\Documents\tmssoftware\TMS MQTT\TMSMQTTPkgDXE13.dproj]
C:\Program Files (x86)\Embarcadero\Studio\21.0\Bin\CodeGear.Delphi.Targets(402,5): error MSB6003: The specified task executable "dcc" could not be run. Filnavnet eller filtypen er for lang [C:\Users\achristo\Documents\tmssoftware\TMS MQTT\TMSMQTTPkgDXE13.dproj]
Done Building Project "C:\Users\achristo\Documents\tmssoftware\TMS MQTT\TMSMQTTPkgDXE13.dproj" (Build target(s)) -- FAILED.
This means your Delphi library path is too long. Please try to sanitize your library path and remove unused paths and then retry to install.
If you have MindManager 21 installed, maybe this could be a starting point to make paths shorter and more likely installing not fals like here 