AFAICT lanes are not shared but there are chipsets which can break lanes out into other sets of lanes which are then routed back onto the original set of lanes. So if your CPU has 16 lanes you can hang a chip off of it which then provides more lanes which are then signaled back to the CPU over some subset of those lanes.
It’s not clear if the lanes themselves can be multiplexed with packets from many devices but they can change the number of assigned lanes after initialization so a clever chipset could probably dynamically allocate lanes as used.
motherboard features such as x16 or 2x8 are achieved with "pcie mux" chips. these are devices which select which of N pairs of differential wires is attached to the input/output differential pair. search for "pcie mux" will find many, such as [0]. if you look at the diagram you'll see that it connects wire pair A+/A- to either B+/B- or C+/C- based on the value of the SEL line.
these generally basic passive devices operating at analog signals level, no higher layer activity required. however some may exist which operate as "retimers", which do participate in the lowest layer of the PCIe electrical protocols (generally to extend reach). these are unlikely to be used for a typical x16 <-> 2x8 sort of motherboard feature though.
the example i picked here is 4 lanes, and you would need 4 such chips to do a x16 <-> 2x8. (spoiler: you mux lanes 8-15 from slot X to lanes 0-7 of slot Y, and there are both TX and RX pairs which need muxing.)
there do exist devices called "pcie switches" which operate at all layers of the pcie protocols, and allow for all sorts of sharing of the point-to-point links. examples at microsemi [1] ... for example a 48 lane switch could be used to connect two 16 lane GPUs to a 16 lane slot. this would allow either of the GPUs to burst to the full 16 lanes, or on average if both GPUs are communicating with the host then they would see 8 lanes of bandwidth. there's a picture of such a dual GPU card in this article [2], you can see the PCIe switch ASIC centered in between the two GPUs, above and to the right of the edge connector.
> It’s not clear if the lanes themselves can be multiplexed with packets from many devices
They can be, this is what the chipsets do on most platforms. AMD's X570 splits out 4x gen4 PCI-E lanes into 8x gen4 PCI-E lanes + a bunch of other stuff: https://i.imgur.com/8Aug02l.png
Intel's been doing this better and is what their marketing calls "platform lanes" - the Z390 for example provides 24 PCI-E gen3 lanes from what is essentially a single 4x gen3 uplink to the CPU: https://images.anandtech.com/doci/12750/z390-chipset-product... (DMI 3.0 is essentially PCI-E x4 gen3 in all but name)
It’s not clear if the lanes themselves can be multiplexed with packets from many devices but they can change the number of assigned lanes after initialization so a clever chipset could probably dynamically allocate lanes as used.