Why would you need a travel router?
The rpi already can be set up to hotspot it’s own wifi network.
For connecting to hotel wifi, a simple usb dongle is good enough, as discussed here: https://forums.raspberrypi.com/viewtopic.php?t=287485
In regards to VPN-ing into the media server at home - depending on where you travel, you might not have any internet or you might use up your mobile data volume.
What the fuck did I just read? Some AI hallucination?