Is it possible to connect two external 4K60 monitors to a M1 Pro macbook using a single Thunderbolt 4 port, more specifically using a dock?
No, it's not possible. There are exceptions that I'll get into but generally no, that is not possible. This has been a long time complaint of Apple computers and it does not appear Apple is going to change this.
The main issue is Apple does not support MST, multi-stream transport, over DisplayPort. This means one port supports only one display.
Apple states on their website that computers with M1 and Thunderbolt 4 support only one display per port. It's in their support page on connecting displays: https://support.apple.com/en-us/HT202351
And on identifying ports: https://support.apple.com/en-us/HT201736
The exceptions to this are displays controlled by a separate GPU. Someone could plug in a dock with a DisplayPort output and USB, and then use a USB GPU like those made by DisplayLink to drive the second display. Some docks have DisplayLink GPUs built-in to them for multiple displays. Another means to get an external GPU is with a box that is clearly labeled an external GPU. These are docks with a primary function of adding additional graphics processing, though this processing is available to be used on an internal display as well as external displays. These eGPU docks will tend to have other ports like USB and Ethernet but some do not as their function is to be a GPU, not a general purpose dock, and so may lack such ports as they take valuable bandwidth.
If connecting two displays by one Thunderbolt cable is important to you then you are going to have to pay for it. There is no cheap resolution to this. Windows will support two displays on a single Thunderbolt port but you pay for it in a different way, lower video performance. Two 4K@60 displays on one Thunderbolt port is asking a lot, if it works at all then it's likely by "cheating" with compressed video. Maybe the math works out and no cheating required but it's getting real close to the limits of the cables.
DisplayLink and eGPU get by with less bandwidth on the cable to the computer because the video is still a stream of descriptive bits at that point. After processing into the full uncompressed video frame there's more data. After processing there is more bandwidth consumed on the cable to the display, one 4K@60Hz consumes more data than one DisplayPort channel can hold. Supporting two 4K displays means using all 4 "superspeed" channels in the USB-C cable for video, leaving no channels for Thunderbolt or USB 3.x, or multiplexing the DisplayPort video into the same "superspeed" channels, which is a feature not all displays and docks support. I speculate but it's likely safe to assume Apple didn't want to confuse users with the long list of technical requirements on what is needed to get two displays on one Thunderbolt port to work and simply says it is not supported. They "enforce" this limitation by not including MST support in their OS and drivers, without MST there's no multiplexing two DisplayPort streams on one cable.