ASUS ZenScreen Touch Screen 15.6” 1080P Portable USB (MB16AMT) - Full HD (1920 x 1080), IPS, Anti-glare, Built-in Battery, Speakers, Eye Care, USB Type-C, Micro HDMI, Smart Case, 3-Year Warranty

I went with a portable monitor, and went high end (in 2020) - Asus ZenScreen MB16AMT - 15.6", 10 point touch, built in battery. The reason I went all out - my company paid for it during the pandemic. I use it with my S21 Ultra, and with my Windows laptop. Its great when traveling, I leave the laptop at home, and bring the ZenScreen, a bluetooth keyboard and a bluetooth mouse. Today, if I were to do it again, I would probably invest in a NexDock instead.

Nice compact setup, similar to mine. I imagine that if the monitor does not have a battery, it will drain your phone battery quite quickly though. I've got the Asus ZenScreen MB16AMT, which has battery, touch screen, and speakers. The monitory can run on battery for 4+ hours without pulling power from the phone. (S21 Ultra) For longer usage, I added an Anker 555 hub, 45w PD charger, and run hdmi and usb-c to my monitor (the hub cannot do usb-c video output). Dual cables gets power to the monitor, touch support, and video via hdmi.

ive got an mb16amt, wheich has the battery, and the s21 ultra. no problems going ubc-c to the monitor, since it will run on battery. i've also got an anker 555 hub (powered by a 45w pd charger), which does not pass through display through USB-c, so I run hdmi to the monitor. But then I also plug in usb-c to the monitor, which allows the touch to function, and to keep the monitor powered and charged, and to keep the s21 powered fully. maybe your answer is to get a hub that supports PD passthrough and hdmi?

I'm currently using an ASUS ZenScreen MB16AMT that also has a battery and touchscreen. Also, based on your budget, there are several other Zenscreen models that might meet your requirements