Add the missing APN into the interface configuration and check if you have correct APN set on the modem with AT+CGDCONT?
Try setting plmn (MCC and MNC) for the local operator as shown in the wiki, perhaps you can see the best one on your phone.
https://openwrt.org/docs/guide-user/network/wan/wwan/ltedongle#qmi_protocol_configuration_parameters
Do not run uqmi manually, check what is in the system log after you restart the interface.
this didn't changed anything, I think the APN was selected correctly in past automatically.
Anyway some success, after changing the SIM back to the one I just used in my GL-iNet, the connection was established and I even got internet with it - yesterday evening.
Today it tells me:
SIM status Registered (roaming)
Connection statistics 0d, 00:09:19
Technology LTE B20 (800 MHz)
I have an ip on wwan0 I can ping, I have a default route on that interface I can not ping and I can not ping anywhere else. So right now I have no idea what's going wrong 
(Sure, I tried restarting, power off, etc. without success)
What it the reason for not doing so? It's because it blocks sometimes with no output, when I try to run it on the cli?
And I have an other problem with devices, that do not connect to the wifi ...
Did you try switching to another operator using plmn option? See if you can get a better band like 3 or 7.
When uqmi is called from the connection script the latter is taking care about setting and getting client-id on each transaction. When triggered manually, the action is performed "out of sequence" and may produce unexpected results.
P.S. My personal choice for this device is Nordic B12 router firmware and a bridge mode.
Hi,
new "status", new country with new roaming provider, same SIM and same configuration and it's working currently more or less.
That means, that I can establish an internet connection, get IP and default gateway and also can reach the internet, what was not possible before.
But still I can not ping the default gateway ip, maybe, this is blocked somewhere.
And it's not always reliable, twice I had to restart the router, to get a connection.
Next (and final) step will be the use of a SIM from a local provider (it's working perfectly in my GL-iNet since 2 years), so hopefully everything is working then.
So you do not use "standard" OpenWrt but a provider firmware?
Unfortunately that's not an option for me, because I need some extra functionality, that I can get with OpenWrt. Without this, I would have to add a Raspi behind the router to get this. With the GL-iNet-router I have to do this, because I didn't got working the OpenVPN-tunnel directly on the router, that's (and some other stuff) running on the Raspi now.
Kind regards,
thg
okay, final comment about this:
With the prepaid-SIM card of a local provider it just works. No problems, no restarts, connects automatically as expected.
So I assume problems with EU-roaming, that where not handled correctly by the router.
Thanks to all for the hints, kind regards, thg