networking – Ethernet installation in New house using Legrand TM1110 Terminal Telephone Input Module


I recently moved to a new house and it is pre wired with ethernet. Today, I finally decided to check out the wiring in order to connect an additional Wireless Access point in a different room. My Internet router provided by my ISP has a built in switch with about 6 additional ports so I decided to connect an Ethernet cable from one of the ports to the Ethernet Jack on the wall thinking I would be able to get the signal in any other jack in the house, unfortunately that was not the case. So I bought a tone tracer and determined (!(unpatched cable)(1))(1) the cable is not actually connected to anything (see picture below with circled unpatched cable).

So, my question is, in order to Provide Ethernet Access with Internet to the rest of the house, do I have to patch this cable to the Legran TM1110 terminal Service In slot? (!(Legrand Terminal)(2))(2)
Will this actually work? I also see there is an Ethernet Jack in this Legran Terminal, what’s that for? Can I terminate the cable with an Ethernet jack and plug it there.

In any case, what’s the best solution? Last resort I can also always install an actual switch in there since there is a power outlet, and terminate all the cable with jacks but I suspect there must be a better solution.

Thanks!
(1): https://i.stack.imgur.com/3pgal.jpg
(2): https://i.stack.imgur.com/f4mZ0.jpg