The screenshot shows you are using google dns. I can use 8.8.8.8 on my box and resolve the names that you cannot.
If I were in your shoes, I would want to see if it was a true dns issue across the network:
on a networked machine: ping those servers you cannot resolve on the meteobridge
ping rtupdate.wunderground.com
ping data.awekas.at
ping www.empw.net
if they resolve, then we most likely have some other network misconfiguration(mtu size mismatch, some restriction in the router, ipv6).
Edit: reading a ton about dns issues(especially with google dns), dual-stack issues, and other network maladies with T-Mobile.
I think you may want to see if Verizon 5G works in your area with all that trouble.
insofar as updating your MR3020 to the latest, if you really want to do that before figuring out the network issue:
When you need to flash a new Meteobridge firmware to your TL-MR3020, TL-MR3040, TL-WR703N or DIR-505, you can do that by calling the URL "http://ip-of-your-meteobridge/cgi-bin/fwupdate.cgi". This will shutdown some running services and will bring you to the openwrt SW stack below Meteobridge application software stack.
If your device cannot load Meteobridge application stack from the Internet for some reason, you can also directly access openwrt web interface by browsing to "http://ip-of-your-meteobridge-device/cgi-bin/luci".
Login with your Meteobridge password and go to "System" tab. Select sub tab "Backup / Flash Firmware" and use offered "Flash new firmware" section.
Unmark "keep settings" option and start flashing. Keep device connected to power, it will restart automatically. If you have a WL-330N3G, this always needs to be flashed with the TFTP environment as in setup section for that device explained.