The M1 IMac has TB4/USB4 and USB-C ports. The nomenclature is misleading, because in the world of USB these days, the number (eg the 4 in USB4) refers to speed while the letter (C in USB-C) refers to the physical connections. Further, Thunderbolt 4 is basically Thunderbolt 3 with the full TB specification implemented, and since Apple had actually supported the full TB specification in its TB3 ports, the only real change is that Big Sur now supports TB hubs (which, btw, a TB3 port on an older Mac will also support under Big Sur). There is a good description of the TB3/4 issue by the head honcho at OWC if anyone is interested.
In any case, you have (unless you bought the very lowest end iMac) two TB/USB4 ports and two USB-C ports. All of them are capable of supporting an external display, although you can only attach one external display in total. Which you use depends in part on your display. If you had a display with USB-C connectivity you could actually connect it to any of the ports, because all 4 will support display over USB-C protocols. If you have a Thunderbolt Display you can ONLY connect to a TB/USB port because the display protocol is handled differently and USB-C ports don’t support the protocol used by TB monitors. If you have anything else (HDMI, DisplayPort, etc) you could again connect to any port, provided you used the correct cable (eg USB-C to DP).
Since you have a display that connects via TB1, it has to be connected to a TB port. The Apple TB3<->TB2 adaptor will work. It turns out this adapter is bidirectional (as far as I am aware it is the only such connector on the market this bidirectional) and so can be used to connect a TB2 device to a TB3 port on the computer OR a TB3 device to a TB2 port on the computer. Transfer speed is of course limited to the slowest device connected.
Since the TB1 port connector is identical to the TB2 connector, and TB2 devices are backward compatible to TB1, you should be able to connect the adapter to a TB3 port on your iMac and then connect the monitor to the TB2 end of the adapter.