There's no shortage of ways to manage your data, whether it's an external SSD or HDD, a home NAS server, or buying a higher-storage variant of your phone. I have a DiskStation DS1823xs+ that stores over 150TB of my data, but when I'm on the go, I rely on external SSDs.
TeamGroup does a great job in this area, and its X2 Max is what I predominantly use while traveling. It resembles a USB flash drive, but it houses an SSD, and it has both USB-C and USB-A connectors, allowing me to connect it to just about any device. And coming in at $149 for the 1TB variant, it's a decent choice if you want a fast external drive.