Hi!
As far as I know it is not possible to completely omit the Home Box (in your case the Technicolor FGA2233) given by Telekom. It would be also good to know whether you also have any TV packages provided by Telekom.
However, if you want to use your own device, you can add it to your current setup. In order to do this you need to enable the PPPoE passthrough mode in the Technicolor Home Box. Open up a web browser [e.g. Edge, Chrome, Firefox etc.] and type into the addrss bar: 192.168.1.1 , then press Enter. A Sign In page will appear. Your username is: admin by default. Your passowrd can be found on a sticker which is likely on the buttom of the device. Look for the phrase: "Access Key". What is written after that that is your password. The Username is there too (as I've mentioned most likely it is "admin"). After signing in, look for PPPoE passthrough option, and turn it on. WIFI should be turned off on Technicolor. [And this is where it would be good to know whether you also have any TV subscription plans by Telekom or not. The Telekom Smartbox requires a router with IGMP support. [If your FRITZ!Box 5590 does not support this, then the Smartbox can only be connected to Technicolor.] In your Technisat device you should find the necessarry credentials. Write these down! That way later you can easily change the settings back if something does not work as it should! In the forum many suggests that you should erase these credentials from Technicolor, and then save the modifications. Then enter the PPPoE data into your Fritz!Box 5590, and save them. And it is possible that you have to switch off and then back on the PPPoE mode, because for the first try it seems that is not always successful.
How to connect the devices:
Persumably your Technicolor device currently connects to a PC (laptop, desktop) through one of its LAN ports (e.g. LAN1). To add your device to the setup you need to connect your own device with Technicolor. To do this plug one end of the LAN cable into your FRITZ!Box 5590 WAN port (1 X 2.5 Gigabit) and the other end should go into the Technicolor's LAN1 port.
Now you should be able to use your own device.
As for 1414: do not worry about they saying things in Hungarian! Wait, and when the operator answers, start the conversation in English!
I also suggest to try and use chat function on the website if you need any help. As far as I know Vanda does not speak English, but when it offers the first possibility to write your prompt, you should write something like: "szerződés" [contract]. In this topic it cannot help so it directs you to a live assistant, with whom you can discuss your problem in English.
I hope I could help.
Best wishes,
Adam