Thunderbolt 3 splitter?

One reason ThunderBolt-3 is fast is because electrically, it is point-to-point. It was originally intended for fiber-optic connection, and using 'only' expensive copper cabling (rather than stops-your-heart-expensive fiber optic cabling) is already a compromise. You will not find splitters available.

Unless/Until you find a dock that appeals to you (and more are appearing every week) that is the only solution other than buying a more-capable Mac.

I took another look at one (less than US $40) and it only had one Thunderbolt 3 port, so that would likely just be for connection to the computer. Even the more expensive ones with two Thunderbolt 3 ports would be good just for one as a pass through after connecting the other to a Mac. You would really need something with at least 3 Thunderbolt 3 ports.

I looked up the ExpressDock HD and CalDigit TS3. They won't even do what you're looking for. They only have two Thunderbolt 3 ports. So you might be able to plug in one port to your computer and then use the other one for something that needs Thunderbolt 3. Those are primarily designed to connect to USB 3.0, SD, DisplayPort, etc. while providing one available Thunderbolt 3 port for an external peripheral.

I don't believe there's any kind of "splitter" that would do what you're looking for either. It would have to be an active hub with electronics to route the signals. A passive splitter wouldn't work.

Mostly what's inexpensive will be USB-C hubs. There might be some relatively inexpensive docks with a single Thunderbolt 3 capable port along with USB-C and USB-A ports.