Looking at picture you have a on/off to left and two way to right, I see no neutral wire on original, the new switch seems to require a neutral, and seems to have no option to use for two way switching.
To get two way switching normally the second switch also needs changing to a slave type switch. There are smart switches which allow a remote which looks like a switch so you get two way switching, there are also versions that work without a neutral.
However if there is no neutral often there is also a minimum bulb size, I know my Energenie will work with 10W but some other makes need 15W, also my Energenie comes as a single switch only so not suitable for you. (It also requires an expensive hub to work with phone.)
I do see the idea of Smart switches, you can set them up so they geofence or you simply switch on with phone, I fitted mine as a lazy way of setting up two way switching, saved me threading cables, but for hall I have a cheap Lidi rechargeable torch plugged into a socket above the door to under stairs, best thing we have every had lighting wise, although not originally bought to do this, with a power cut it lights so I can remove it and inspect the consumer unit, and at night it has a built in PIR which is enough to see by to walk along the hall, lighting our way in. It also help when coming down stairs at night, and up once main hall light switched off, socket originally placed to charge mobility scooter, and light originally for caravan, but it works so well got another for caravan.
What do you want? maybe an easy way to do it, without rewiring switch to include a neutral, mine was selected as also had sockets and TRV heads on same system.
