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In my case it went from a patchy 1mbps to a stable 20mbps right away, according to my router's admin page - right after resoldering the resistor and connecting the antenna.

Resoldering the 0 ohm resistor was like an adventure, but somehow managed to connect the correct pins. The end result looks like following:

https://imgur.com/a/LJflZ80

Yes, from my experience with this project the external antenna is a must. I've update the README with a link to the one I used.

Can you recommend an exact model?

I'm afriad not, I bought a load of esp32 cams with out the external antenna - hit a problem with the frame rate and fixed it from the advice from the link

for my other projects I did use a ESP32 with an external antenna, but they did not have a camera port

These things are so cheap just buy one and see (unless time is an issue)

edit: the OP did add this link to one https://www.aliexpress.com/item/1005001468076374.html - note this does not have a usb connector - you can get them separately